User interface for a financial advisory system

ABSTRACT

A method and an apparatus for a user interface for a financial advisory system is provided. According to one embodiment of the invention, a set of one or more input objects and a set of output values are displayed. The input objects include an indication of a target retirement age, an indication of a target level of investment risk, and an indication of a retirement income goal. The output values include an indication of the probability of achieving the retirement income goal and an indication of the most likely retirement income in current dollars. After updated values for the input decisions are received via one or more of the input objects, one or more new output values are determined based upon the updated input decisions. The set of output values is then refreshed to reflect the one or more new output values.

[0001] This is a continuation of application Ser. No. 09/495,982, filedon Feb. 1, 2000, that is currently pending, which is acontinuation-in-part of U.S. Pat. No. 6,012,397, filed on Dec. 2, 1997.

COPYRIGHT NOTICE

[0002] Contained herein is material that is subject to copyrightprotection. The copyright owner has no objection to the facsimilereproduction of the patent disclosure by any person as it appears in thePatent and Trademark Office patent files or records, but otherwisereserves all rights to the copyright whatsoever.

BACKGROUND OF THE INVENTION

[0003] 1. Field of the Invention

[0004] The invention relates generally to the field of financialadvisory services. More particularly, the invention relates to a systemfor advising a user regarding feasible and optimal portfolio allocationsamong a set of available financial products and a user interface forsuch a system.

[0005] 2. Description of the Related Art

[0006] During the 1980's, a significant trend emerged in retirementsavings. Traditional defined benefit plan assets began shifting towardsemployee-directed defined contribution plans like 401(k). As this trendcontinues, many individual investors will ultimately become responsiblefor managing their own retirement investments. However, many people arenot well-equipped to make informed investment decisions. Further, thenumber and diversity of investment options available to individuals israpidly increasing, thereby making investment decisions more complex bythe day.

[0007] Many investment software packages claim to help individuals planfor a secure retirement, or some other intermediate goal. However,typical prior art investment software packages are limited in severalways. For example, some packages provide generic asset-allocationsuggestions (typically in the form of a pie-chart) and leave theinvestor to find the actual combination of financial products that meetsthe suggested asset allocation. However, many investments available toindividual investors, such as mutual funds, cannot easily be categorizedinto any one generic asset class category. Rather, mutual funds aretypically a mix of many different asset classes. This property of mutualfunds complicates the selection of appropriate instruments to realize adesired asset allocation.

[0008] Further, some prior art programs, typically referred to as“retirement calculators,” require the user to provide estimates offuture inflation, interest rates and the expected return on theirinvestments. In this type of prior art system, the user is likely, andis in fact encouraged, to simply increase the expected investmentreturns until their desired portfolio value is achieved. As should beappreciated, one of the problems with this type of program is that theuser is likely to create an unattainable portfolio based on anunrealistic set of future economic scenarios. That is, the portfolio offinancial products required to achieve the X % growth per year in orderto meet the user's retirement goal may not be available to the user.Further, the idealistic future economic conditions assumed by the user,for example, 0% inflation and 20% interest rates, may not bemacroeconomically consistent. Typical prior art investment packagessimply allow the user to manipulate economic conditions until a desiredresult is achieved rather than encouraging the user to focus on his/herown decisions regarding investment risk, savings rate, and retirementage within the context of realistic economic assumptions. Consequently,the so called “advice” rendered by many of the prior art investmentsoftware packages can be misleading and impossible to implement inpractice.

[0009] In addition, investment advice software and their user interfacesin the prior art have various other disadvantages which are overcome bythe present invention. Notably, prior art systems typically do notprovide realistic estimates of the investment or retirement horizonrisk-return tradeoff given a user's specific investments and financialcircumstances. This makes informed judgments about the appropriate levelof investment risk very difficult. The notion of a risk-return trade offis fundamental to modern portfolio theory, and any system which fails toconvey long-term risk and return fails to provide information essentialto making informed investment decisions.

[0010] In view of the foregoing, what is needed is a financial advisorysystem that employs advanced financial techniques to provide financialadvice to individuals on how to reach specific financial goals, focusesindividuals on the financial decisions they must make today, recommendsone or more specific financial products given these decisions, andillustrates the chance that the financial decisions combined with therecommended financial products will meet their needs in the future. Morespecifically, it is desirable to provide a system that automaticallygenerates future-looking realistic economic and investment returnscenarios and allows a user to arrive at a feasible portfolio that meetsboth intermediate and long-term financial goals by a process ofoutcome-based risk profiling. In this manner, the user can focus onhis/her own decisions regarding investment risk, savings, and retirementage while interactively observing the impact of those decisions on therange of possible investment outcomes. Further, it is desirable that thefinancial advisory system create a feasible optimal portfolio thatmaximizes the utility function of the user by selecting financialproducts that are available to the user and that provides the highestpossible utility given the user's risk tolerance, investment horizon andsavings level. By utility what is meant is a function that determinesthe relative preferences of an individual for different combinations offinancial products based on one or more characteristics of the products(e.g., expected return, variance, etc.), and optionally one or moreparameters specific to the individual. Moreover, it is advantageous toperform plan monitoring on an ongoing basis to alert the user if thelikelihood of meeting their financial goals falls below a thresholdvalue or if their portfolio risk level becomes inconsistent with theirrisk preferences. It is also desirable to provide specific advice to theuser regarding steps they can take to improve their chances of meetingtheir financial goals while taking into consideration the user'spersonal tradeoffs among risk, savings, and retirement age.

[0011] Finally, it is also desirable to incorporate an intelligent userinterface that communicates the fundamental risk-return tradeoffs tohelp individuals evaluate investment options. For example, it isdesirable to provide a system that provides a visual indicationrepresentative of the probability of achieving a financial goal ratherthan a binary result. Also, it is advantageous to calibrate graphicalinput mechanisms so that the range of inputs allowable by thesemechanisms are in fact feasible based upon available products.Additionally, to provide the user with the opportunity to make informedchoices among an available set of financial products, it is desirable topresent realistic estimates of risk based on projected outcomesassociated with the specific recommended financial products.Importantly, because there is no one way that people look at risk, it isalso desirable to present various notions of risk such as short-termrisk, long-term risk, and the risk of not reaching a particularfinancial goal.

SUMMARY OF THE INVENTION

[0012] A financial advisory system and a user interface for such asystem is described. According to one aspect of the present invention,return scenarios for optimized portfolio allocations are simulatedinteractively to facilitate financial product selection. Returnscenarios for each asset class of a plurality of asset classes aregenerated based upon estimated future scenarios of one or more economicfactors. A mapping from each financial product of an available set offinancial products onto one or more asset classes of the plurality ofasset classes is created by determining exposures of the available setof financial products to each asset class of the plurality of assetclasses. In this way, the expected returns and correlations of aplurality of financial products are generated and used to produceoptimized portfolios of financial products. Return scenarios aresimulated for one or more portfolios including combinations of financialproducts from the available set of financial products based upon themapping.

[0013] According to a second aspect of the present invention, a user mayinteractively explore how changes in one or more input decisions affectone or more output values. A first and second visual indication areconcurrently displayed. The first visual indication includes inputmechanisms for receiving input decisions and the second visualindication includes a set of output values that are based upon the inputdecisions and a recommended set of financial products. In oneembodiment, these output values include the projected future value ofthe recommended financial products and the chance that the user meetshis/her goals. After updated values for the input decisions are receivedvia the input mechanisms, a new recommended set of financial productsand a new set of output values may be determined based upon the updatedvalues. At which point, the second visual indication may be updated toreflect the new set of output values. In this manner, the user isfocused on the relevant decisions that can be made to reach one or morefuture financial goals and the effects of modifying one or more of thedecisions.

[0014] According to a third aspect of the present invention, a graphicalinput mechanism for receiving a desired level of investment risk may becalibrated. A set of available financial products and a predefinedvolatility are received. The settings associated with the graphicalinput mechanism are constrained based upon the set of availablefinancial products. As a result, the user is prevented from selecting alevel of risk that is outside of the feasible set of risk that isactually available. Additionally, the calibration of the units of thegraphical input mechanism may be expressed as a relationship between thevolatility associated with a setting of the graphical input mechanismand the predefined volatility.

[0015] According to a fourth aspect of the present invention, anindication is provided to the user of the probability of achieving afinancial goal. A financial goal is received from the user. In addition,inputs upon which a probability distribution is dependent are received.The probability distribution may represent a set of possible futureportfolio values, for example, based upon the inputs. The probability ofachieving the financial goal is determined by evaluating the cumulativeprobability distribution that meets or exceeds the financial goal.Finally, a visual indication may be provided to the user of theprobability of achieving the financial goal.

[0016] According to a fifth aspect of the present invention, variousaspects of financial risk are presented to the user in order to help theuser deal with and control financial risk. A financial goal is receivedfrom the user. In addition, inputs including decision variables uponwhich a probability distribution is dependent are received. Theprobability distribution may represent probabilities over time of theuser having a certain amounts of wealth, for example. A first and secondvisual representation are displayed. The first visual representationillustrates a risk of not achieving the financial goal based upon theprobability distribution and the second visual representationillustrates a short-term risk of how much the portfolio value mightdecline in the near future. Additionally, a third visual representationmay also be displayed to illustrate the long-term financial riskassociated with the decision variables. Advantageously, risk isexpressed in terms of outcomes that may result from specific decisionsand financial products thereby enabling the user to select the amount ofrisk consistent with his/her risk preference.

[0017] According to a sixth aspect of the present invention, arecommended allocation of wealth among an available set of financialproducts is presented to the user. Decision inputs and a set ofavailable financial products are received. Each of the financialproducts has an associated volatility. The set of available financialproducts are ordered by their respective volatilities. A recommendedallocation of wealth is determined for each financial product based uponthe decision inputs and a graphical indication is displayed of therecommended allocation of wealth. The graphical indication includesgraphical segments associated with each financial product which havelengths corresponding to the recommended allocation of wealth to theparticular financial product.

[0018] According to a seventh aspect of the present invention, arecommendation may be updated based upon a user specified constraint. Agraphical indication of a current recommended allocation of wealth amongan available set of financial products is provided to the user. Thegraphical indication includes graphical segments each having a sizecorresponding to the current recommended allocation for the associatedfinancial product. A selected graphical segment may be resized tocorrespond in size to a user-desired allocation responsive to activationof an input device. Subsequently, a new set of financial products arerecommended while keeping the allocation of the financial productcorresponding to the selected segment fixed at the user desiredallocation. Then, the graphical indication is updated to represent thenew recommended allocation. Advantageously, in this manner, the user maydirectly manipulate the recommended portfolio and observe the impact onthe recommendation.

[0019] Other features of the present invention will be apparent from theaccompanying drawings and from the detailed description which follows.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0020] The present invention is illustrated by way of example, and notby way of limitation, in the figures of the accompanying drawings and inwhich like reference numerals refer to similar elements and in which:

[0021]FIG. 1 illustrates a financial advisory system according to oneembodiment of the present invention.

[0022]FIG. 2 is an example of a typical computer system upon which oneembodiment of the present invention can be implemented.

[0023]FIG. 3 is a block diagram illustrating various analytic modulesaccording to one embodiment of the present invention.

[0024]FIG. 4 is a flow diagram illustrating core asset class scenariogeneration according to one embodiment of the present invention.

[0025]FIG. 5 is a flow diagram illustrating factor asset class scenariogeneration according to one embodiment of the present invention.

[0026]FIG. 6 is a flow diagram illustrating financial product exposuredetermination according to one embodiment of the present invention.

[0027]FIG. 7 is a flow diagram illustrating portfolio optimizationaccording to one embodiment of the present invention.

[0028]FIG. 8 is a flow diagram illustrating plan monitoring processingaccording to one embodiment of the present invention.

[0029]FIG. 9 illustrates an advice summary screen according to oneembodiment of the present invention.

[0030]FIG. 10A illustrates an exemplary set of financial products thatmay be available to a user.

[0031]FIG. 10B illustrates slider bars that may be used forcommunicating values of decision variables according to one embodimentof the present invention.

[0032] FIGS. 11A-C illustrate risk slider bar calibration according toone embodiment of the present invention.

[0033]FIG. 12A illustrates a two dimensional chart which represents arange of possible values of a portfolio of financial products over time.

[0034]FIG. 12B is a cross section of the chart depicted in FIG. 12Awhich illustrates the probability distribution at a particular time.

[0035]FIG. 12C is a set of icons that may be used to communicate thelikelihood of achieving a financial goal according to one embodiment ofthe present invention.

[0036]FIG. 13 is a flow diagram illustrating a method indicating theprobability of achieving a financial goal according to one embodiment ofthe present invention.

[0037]FIG. 14 illustrates a graphical device which may be employed tocommunicate long-term financial risk according to one embodiment of thepresent invention.

[0038]FIG. 15 illustrates a graphical device which may be employed tocommunicate long-term financial risk according to one embodiment of thepresent invention.

[0039]FIG. 16 is a flow diagram illustrating a method of depictingrecommended financial product portfolios according to one embodiment ofthe present invention.

[0040]FIG. 17A illustrates a graphical device that may be used tocommunicate the current optimal portfolio allocation based upon thecurrent state of the decision variables and other inputs according toone embodiment of the present invention.

[0041]FIG. 17B illustrates the graphical device of FIG. 17A after therisk decision variable has been increased according to one embodiment ofthe present invention.

[0042]FIG. 18 is a flow diagram illustrating a method of updating arecommended portfolio based on a user specified constraint according toone embodiment of the present invention.

[0043]FIG. 19A illustrates a graphical device that may be used tocommunicate the current optimal portfolio allocation based upon thecurrent state of the decision variables according to one embodiment ofthe present invention.

[0044]FIG. 19B illustrates the graphical device of FIG. 19A after theuser has imposed a constraint upon one of the financial products.

DETAILED DESCRIPTION OF THE INVENTION

[0045] A financial advisory system and a user interface for such asystem is described. In embodiments of the present invention, a factormodel approach is laid on top of a pricing kernel model to simulatereturns of a plurality of asset classes, and ultimately financialproducts, such as securities or portfolios of securities. The term“financial products” as used herein refers to a legal representation ofthe right (often denoted as a claim or security) to provide or receiveprospective future benefits under certain stated conditions. In anyevent, the forecasts may then be used for purposes of providingfinancial advisory services to a user. For example, such forecasts areuseful for selecting the composition of an optimized portfolio (based ona utility function) from a set of available financial productsconditional on decisions and constraints provided by the user.

[0046] Briefly, fundamental economic and financial forces are modeledusing a pricing kernel model that provides projected returns on aplurality of asset classes (core asset classes) conditional on a set ofstate variables that capture economic conditions. The core asset classesin combination with additional asset class estimates that areconditioned on the core asset classes comprise a model (hereinafter “thefactor model”) of a comprehensive set of asset classes that span theuniverse of typical investment products. A factor model is areturn-generating function that attributes the return on a financialproduct, such as a security, to the financial product's sensitivity tothe movements of various common economic factors. The factor modelenables the system to assess how financial products and portfolios willrespond to changes in factors or indices to which financial products areexposed. The selection of asset classes may be tailored to address anarrow or broad range of investors. For example, asset classes may bechosen that are relevant only to a particular industry or asset classesmay be chosen to span the market range of a broad set of possibleinvestments (e.g. all available mutual funds or individual equities).According to embodiments of the present invention discussed herein, toreach the broadest segment of individual investors, the asset classesselected as factors for the factor model have been chosen to span therange of investments typically available to individual investors inmainstream mutual funds and defined contribution plans.

[0047] After generating future scenarios for the factor model, financialproducts available to an investor may be mapped onto the factor model.To assure that a portfolio recommended by the system is attainable, itis preferable to generate investment scenarios that include only thosefinancial products that are available to the investor. The availablefinancial products may include, for example, a specific set of mutualfunds offered by an employer sponsored 401(k) program. In any event,this mapping of financial products onto the factor model is accomplishedby decomposing the returns of individual financial products intoexposures to the asset classes employed by the factor model. In thismanner, the system learns how each of the financial products availableto the user behave relative to the asset classes employed by the factormodel. In so doing, the system implicitly determines the constraints onfeasible exposures to different asset classes faced by an investor givena selected subset of financial products. Given this relationship betweenthe user's available financial products and the factor model, the systemmay generate feasible forward-looking investment scenarios. A stochasticsimulator may provide information relating to various aspects offinancial risk including the risk of not achieving a particularfinancial goal and short- and long-term financial risks in order to helpa user of the financial advisory system deal with and control suchfinancial risks. The system may further advise the user regardingactions that may be taken (e.g., save more money, retire later, take onadditional investment risk, seek opportunities to expand the investmentset) to achieve certain financial goals, such as particular retirementstandard of living, accumulating a down payment for the purchase of ahouse, or saving enough money to send a child to college. Other aspectsof the present invention allow the user to focus on his/her decisionsregarding investment risk, savings, and retirement age whileinteractively observing the impact of those decisions on the range ofpossible investment outcomes.

[0048] In the following description, for the purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent, however, toone skilled in the art that the present invention may be practicedwithout some of these specific details. In other instances, well-knownstructures and devices are shown in block diagram form.

[0049] The present invention includes various steps, which will bedescribed below. The steps of the present invention may be embodied inmachine-executable instructions. The instructions can be used to cause ageneral-purpose or special-purpose processor that is programmed with theinstructions to perform the steps of the present invention.Alternatively, the steps of the present invention may be performed byspecific hardware components that contain hardwired logic for performingthe steps, or by any combination of programmed computer components andcustom hardware components.

[0050] The present invention may be provided as a computer programproduct which may include a machine-readable medium having storedthereon instructions which may be used to program a computer (or otherelectronic devices) to perform a process according to the presentinvention. The machine-readable medium may include, but is not limitedto, floppy diskettes, optical disks, CD-ROMs, and magneto-optical disks,ROMs, RAMs, EPROMs, EEPROMs, magnetic or optical cards, flash memory, orother type of media/machine-readable medium suitable for storingelectronic instructions. Moreover, the present invention may also bedownloaded as a computer program product, wherein the program may betransferred from a remote computer to a requesting computer by way ofdata signals embodied in a carrier wave or other propagation medium viaa communication link (e.g., a modem or network connection).

[0051] While embodiments of the present invention will be described withreference to a financial advisory system, the method and apparatusdescribed herein are equally applicable to other types of assetallocation applications, financial planning applications, investmentadvisory services, financial product selection services, automatedfinancial product screening tools, such as electronic personal shoppingagents and the like.

[0052] System Overview

[0053] The present invention may be included within a client-servertransaction based financial advisory system 100 such as that illustratedin FIG. 1. According to the embodiment depicted in FIG. 1, the financialadvisory system 100 includes a financial staging server 120, a broadcastserver 115, a content server 117, an AdviceServer™ 110 (AdviceServer™ isa trademark of Financial Engines, Inc., the assignee of the presentinvention), and a client 105.

[0054] The financial staging server 120 may serve as a primary stagingand validation area for the publication of financial content. In thismanner, the financial staging server 120 acts as a data warehouse. Rawsource data, typically time series data, may be refined and processedinto analytically useful data on the financial staging server 120. On amonthly basis, or whatever the batch processing interval may be, thefinancial staging server 120 converts raw time series data obtained fromdata vendors from the specific vendor's format into a standard formatthat can be used throughout the financial advisory server 100. Variousfinancial engines may be run to generate data for validation and qualityassurance of the data received from the vendors. Additional engines maybe run to generate module inputs, model parameters, and intermediatecalculations needed by the system based on raw data received by thevendors. Any calibrations of the analytic data needed by the financialengines may be performed prior to publishing the final analytic data tothe broadcast server 115.

[0055] The broadcast server 115 is a database server. As such, it runsan instance of a Relational Database Management System (RDBMS), such asMicrosoft SQL-Server™, Oracle™ or the like. The broadcast server 115provides a single point of access to all fund information and analyticdata. When advice servers such as AdviceServer 110 need data, they mayquery information from the broadcast server database. The broadcastserver 115 may also populate content servers, such as content server117, so remote implementations of the AdviceServer 110 need notcommunicate directly with the broadcast server 115.

[0056] The AdviceServer 110 is the primary provider of services for theclient 105. The AdviceServer 110 also acts as a proxy between externalsystems, such as external system 125, and the broadcast server 115 orthe content server 117. The AdviceServer 110 is the central databaserepository for holding user profile and portfolio data. In this manner,ongoing portfolio analysis may be performed and alerts may be triggered,as described further below.

[0057] According to the embodiment depicted, the user may interact withand receive feedback from the financial advisory system 100 using clientsoftware which may be running within a browser application or as astandalone desktop application on the user's personal computer 105. Theclient software communicates with the AdviceServer 110 which acts as aHTTP server.

[0058] An Exemplary Computer System

[0059] Having briefly described one embodiment of the financial advisorysystem 100, a computer system 200 representing an exemplary client 105or server in which features of the present invention may be implementedwill now be described with reference to FIG. 2. Computer system 200comprises a bus or other communication means 201 for communicatinginformation, and a processing means such as processor 202 coupled withbus 201 for processing information. Computer system 200 furthercomprises a random access memory (RAM) or other dynamic storage device204 (referred to as main memory), coupled to bus 201 for storinginformation and instructions to be executed by processor 202. Mainmemory 204 also may be used for storing temporary variables or otherintermediate information during execution of instructions by processor202. Computer system 200 also comprises a read only memory (ROM) and/orother static storage device 206 coupled to bus 201 for storing staticinformation and instructions for processor 202.

[0060] A data storage device 207 such as a magnetic disk or optical discand its corresponding drive may also be coupled to computer system 200for storing information and instructions. Computer system 200 can alsobe coupled via bus 201 to a display device 221, such as a cathode raytube (CRT) or Liquid Crystal Display (LCD), for displaying informationto a computer user. For example, graphical depictions of expectedportfolio performance, asset allocation for an optimal portfolio, chartsindicating retirement age probabilities, and other data types may bepresented to the user on the display device 221. Typically, analphanumeric input device 222, including alphanumeric and other keys,may be coupled to bus 201 for communicating information and/or commandselections to processor 202. Another type of user input device is cursorcontrol 223, such as a mouse, a trackball, or cursor direction keys forcommunicating direction information and command selections to processor202 and for controlling cursor movement on display 221.

[0061] A communication device 225 is also coupled to bus 201 foraccessing remote servers, such as the AdviceServer 110, or other serversvia the Internet, for example. The communication device 225 may includea modem, a network interface card, or other well-known interfacedevices, such as those used for coupling to an Ethernet, token ring, orother types of networks. In any event, in this manner, the computersystem 200 may be coupled to a number of clients and/or servers via aconventional network infrastructure, such as a company's Intranet and/orthe Internet, for example.

[0062] Exemplary Analytic Modules

[0063]FIG. 3 is a simplified block diagram illustrating exemplaryanalytic modules of the financial advisory system 100 according to oneembodiment of the present invention. According to the embodimentdepicted, the following modules are provided: a pricing module 305, afactor module 310, a financial product mapping module 315, a taxadjustment module 320, an annuitization module 325, a simulationprocessing module 330, a portfolio optimization module 340, a userinterface (UI) module 345, and a plan monitoring module 350. It shouldbe appreciated that the functionality described herein may beimplemented in more or less modules than discussed below. Additionally,the modules and functionality may be distributed in variousconfigurations among a client system, such as client 105 and one or moreserver systems, such as the financial staging server 120, the broadcastserver 115, or the AdviceServer 110. The functionality of each of theexemplary modules will now be briefly described.

[0064] An “econometric model” is a statistical model that provides ameans of forecasting the levels of certain variables referred to as“endogenous variables,” conditional on the levels of certain othervariables, known as “exogenous variables,” and in some cases previouslydetermined values of the endogenous variables (sometimes referred to aslagged dependent variables). The pricing module 305 is an equilibriumeconometric model for forecasting prices and returns (also referred toherein as “core asset scenarios”) for a set of core asset classes. Thepricing module provides estimates of current levels and forecasts ofeconomic factors (also known as state variables), upon which theestimates of core asset class returns are based. According to oneembodiment of the present invention, the economic factors may berepresented with three exogenous state variables, price inflation, areal short-term interest rate, and dividend growth. The three exogenousstate variables may be fitted with autoregressive time series models tomatch historical moments of the corresponding observed economicvariables, as described further below.

[0065] In any event, the resulting core asset classes are the foundationfor portfolio simulation and are designed to provide a coherent andinternally consistent (e.g., no arbitrage) set of returns. By arbitragewhat is meant is an opportunity to create a profitable tradingopportunity that involves no net investment and positive values in allstates of the world.

[0066] According to one embodiment, the core asset classes includeshort-term US government bonds, long-term US government bonds, and USequities. To expand the core asset classes to cover the full range ofpossible investments that people generally have access to, additionalasset classes may be incorporated into the pricing module 305 or theadditional asset classes may be included in the factor model 310 and beconditioned on the core asset classes, as discussed further below.

[0067] Based upon the core asset scenarios generated by the pricingmodule 305, the factor module 310 produces return scenarios (alsoreferred to herein as “factor model asset scenarios”) for a set offactor asset classes that are used for both exposure analysis, such asstyle analysis, and the simulation of portfolio returns. The additionalasset classes, referred to as factors, represented in the factor modelare conditional upon the core asset class return scenarios generated bythe pricing module 305. According to one embodiment, these additionalfactors may correspond to a set of asset classes or indices that arechosen in a manner to span the range of investments typically availableto individual investors in mainstream mutual funds and definedcontribution plans. For example, the factors may be divided into thefollowing groups: cash, bonds, equities, and foreign equities. Theequities group may further be broken down into two different broadclassifications (1) value versus growth and (2) market capitalization.Growth stocks are basically stocks with relatively high prices relativeto their underlying book value (e.g., high price-to-book ratio). Incontrast, value stocks have relatively low prices relative to theirunderlying book value. With regard to market capitalization, stocks maybe divided into groups of large, medium, and small capitalization. Anexemplary set of factors is listed below in Table 1. TABLE 1 GroupFactor Cash: Short Term US Bonds (core class) Bonds: Intermediate-termUS Bonds (core class) Long-term US Bonds (core class) US Corporate BondsUS Mortgage Backed Securities Non-US Government Bonds Equities: LargeCap Stock -- Value Large Cap Stock -- Growth Mid Cap Stock -- Value MidCap Stock -- Growth Small Cap Stock -- Value Small Cap Stock -- GrowthForeign: International Equity -- Europe International Equity -- PacificInternational Equity -- Emerging Markets

[0068] At this point it is important to point out that more, less, or acompletely different set of factors maybe employed depending upon thespecific implementation. The factors listed in Table 1 are simplypresented as an example of a set of factors that achieve the goal ofspanning the range of investments typically available to individualinvestors in mainstream mutual funds and defined contribution plans. Itwill be apparent to those of ordinary skill in the art that alternativefactors may be employed. In particular, it is possible to constructfactors that represent functions of the underlying asset classes forpricing of securities that are nonlinearly related to the prices ofcertain asset classes (e.g., derivative securities). In otherembodiments of the present invention, additional factors may be relevantto span a broader range of financial alternatives, such as industryspecific equity indices.

[0069] On a periodic basis, the financial product mapping module 315maps financial product returns onto the factor model. In one embodiment,the process of mapping financial product returns onto the factor modelcomprises decomposing financial product returns into exposures to thefactors. The mapping, in effect, indicates how the financial productreturns behave relative to the returns of the factors. According to oneembodiment, the financial product mapping module 315 is located on oneof the servers (e.g., the financial staging server 120, the broadcastserver 115, or the AdviceServer 110). In alternative embodiments, thefinancial product mapping module 315 may be located on the client 105.

[0070] In one embodiment of the present invention, an external approachreferred to as “returns-based style analysis” is employed to determine afinancial product's exposure to the factors. The approach is referred toas external because it does not rely upon information that may beavailable only from sources internal to the financial product. Rather,in this embodiment, typical exposures of the financial product to thefactors may be established based simply upon realized returns of afinancial product, as described further below. For more backgroundregarding returns-based style analysis see Sharpe, William F.“Determining a Fund's Effective Asset Mix,” Investment ManagementReview, Dec. 1988, pp. 59-69 and Sharpe, William F. “Asset Allocation:Management Style and Performance Measurement,” The Journal of PortfolioManagement, 18, no. 2 (Winter 1992), pp. 7-19 (“Sharpe [1992]”).

[0071] Alternative approaches to determining a financial product'sexposure to the factors include surveying the underlying assets held ina financial product (e.g. a mutual fund) via information filed withregulatory bodies, categorizing exposures based on standard industryclassification schemes (e.g. SIC codes), identifying the factorsexposures based on analysis of the structure of the product (e.g. equityindex options, or mortgage backed securities), and obtaining exposureinformation based on the target benchmark from the asset manager of thefinancial product. In each method, the primary function of the processis to determine the set of factor exposures that best describes theperformance of the financial product.

[0072] The tax adjustment module 320 takes into account tax implicationsof the financial products and financial circumstances of the user. Forexample, the tax adjustment module 320 may provide methods to adjusttaxable income and savings, as well as estimates for future taxliabilities associated with early distributions from pension and definedcontribution plans, and deferred taxes from investments in qualifiedplans. Further, the returns for financial products held in taxableinvestment vehicles (e.g. a standard brokerage account) may be adjustedto take into account expected tax effects for both accumulations anddistributions. For example, the component of returns attributable todividend income should be taxed at the user's income tax rate and thecomponent of returns attributable to capital gains should be taxed at anappropriate capital gains tax rate depending upon the holding period.

[0073] Additionally, the tax module 320 may forecast future componentsof the financial products total return due to dividend income versuscapital gains based upon one or more characteristics of the financialproducts including, for example, the active or passive nature of thefinancial product's management, turnover ratio, and category offinancial product. This allows precise calculations incorporating thespecific tax effects based on the financial product and financialcircumstances of the investor. Finally, the tax module 320 facilitatestax efficient investing by determining optimal asset allocation amongtaxable accounts (e.g., brokerage accounts) and nontaxable accounts(e.g., an Individual Retirement Account (IRA), or employer sponsored401(k) plan). In this manner the tax module 320 is designed to estimatethe tax impact for a particular user with reference to that particularuser's income tax rates, capital gains rates, and available financialproducts. Ultimately, the tax module 320 produces tax-adjusted returnsfor each available financial product and tax-adjusted distributions foreach available financial product.

[0074] The portfolio optimization module 340 calculates the utilitymaximizing set of financial products under a set of constraints definedby the user and the available feasible investment set. In oneembodiment, the calculation is based upon a mean-variance optimizationof the financial products. The constraints defined by the user mayinclude bounds on asset class and/or specific financial productholdings. In addition, users can specify intermediate goals such asbuying a house or putting a child through college, for example, that areincorporated into the optimization. In any event, importantly, theoptimization explicitly takes into account the impact of futurecontributions and expected withdrawals on the optimal asset allocation.Additionally, the covariance matrix used during optimization iscalculated based upon the forecasts of expected returns for the factorsgenerated by the factor module 310 over the investment time horizon. Asa result, the portfolio optimization module 340 may explicitly take intoaccount the impact of different investment horizons, including thehorizon effects impact from intermediate contributions and withdrawals.

[0075] The simulation processing module 330 provides additionalanalytics for the processing of raw simulated return scenarios intostatistics that may be displayed to the user via the UI 345. In the oneembodiment of the present invention, these analytics generate statisticssuch as the probability of attaining a certain goal, or the estimatedtime required to reach a certain level of assets with a certainprobability. The simulation processing module 330 also incorporatesmethods to adjust the simulated scenarios for the effects induced bysampling error in relatively small samples. The simulation processingmodule 330 provides the user with the ability to interact with theportfolio scenarios generated by the portfolio optimization module 340in real-time.

[0076] The annuitization module 325 provides a meaningful way ofrepresenting the user's portfolio value at the end of the term of theinvestment horizon. Rather than simply indicating to the user the totalprojected portfolio value, one standard way of conveying the informationto the user is converting the projected portfolio value into aretirement income number. The projected portfolio value at retirementmay be distributed over the length of retirement by dividing theprojected portfolio value by the length of retirement. Moresophisticated techniques may involve determining how much the projectedportfolio value will grow during retirement and additionally considerthe effects of inflation. In either event, however, these approacheserroneously assume the length of the retirement period is known inadvance.

[0077] It is desirable, therefore, to present the user with a retirementincome number that is more representative of an actual standard ofliving that could be locked in for the duration of the user'sretirement. According to one embodiment, this retirement income numberrepresents the inflation adjusted income that would be guaranteed by areal annuity purchased from an insurance company or syntheticallycreated via a trading strategy involving inflation-indexed treasury bondsecurities. In this manner, the mortality risk is taken out of thepicture because regardless of the length of the retirement period, theuser would be guaranteed a specific annual real income. To determine theretirement income number, standard methods of annuitization employed byinsurance companies may be employed. Additionally, mortalityprobabilities for an individual of a given age, risk profile, and gendermay be based on standard actuarial tables used in the insuranceindustry. For more information see Bowers, Newton L. Jr., et al,“Actuarial Mathematics,” The Society of Actuaries, Itasca, Ill., 1986,pp. 52-59 and Society of Actuaries Group Annuity Valuation Table TaskForce, “1994 Group Annuity Mortality Table and 1994 Group AnnuityReserving Table,” Transactions of the Society of Actuaries, VolumeXLVII, 1994, pp. 865-913. Calculating the value of an inflation-adjustedannuity value may involve estimating the appropriate values of realbonds of various maturities. The pricing module 305 generates the pricesof real bonds used to calculate the implied real annuity value of theportfolio at the investment horizon.

[0078] Referring now to the plan monitoring module 350, a mechanism isprovided for alerting the user of the occurrence of variouspredetermined conditions involving characteristics of the recommendedportfolio. Because the data upon which the portfolio optimization module340 depends is constantly changing, it is important to reevaluatecharacteristics of the recommended portfolio on a periodic basis so thatthe user may be notified in a timely manner when there is a need forhim/her to take affirmative action, for example. According to oneembodiment, the plan monitoring module 350 is located on theAdviceServer 110. In this manner, the plan monitoring module 350 hasconstant access to the user profile and portfolio data.

[0079] In one embodiment, the occurrence of two basic conditions maycause the plan monitoring module 350 to trigger a notification or alertto the user. The first condition that may trigger an alert to the useris the current probability of achieving a goal falling outside of apredetermined tolerance range of the desired probability of a achievingthe particular goal. Typically a goal is a financial goal, such as acertain retirement income or the accumulation of a certain amount ofmoney to put a child though college, for example. Additionally, the planmonitoring module 350 may alert the user even if the current probabilityof achieving the financial goal is within the predetermined tolerancerange if a measure of the currently recommended portfolio's utility hasfallen below a predetermined tolerance level. Various other conditionsare contemplated that may cause alerts to be generated. For example, ifthe nature of the financial products in the currently recommendedportfolio have changed such that the risk of the portfolio is outsidethe user's risk tolerance range, the user may receive an indication thathe/she should rebalance the portfolio. Plan monitoring processing,exemplary real world events that may lead to the above-described alertconditions, and additional alert conditions are described further below.

[0080] The UI module 345 provides mechanisms for data input and outputto provide the user with a means of interacting with and receivingfeedback from the financial advisory system 100, respectively. Furtherdescription of a UI that may be employed according to one embodiment ofthe present invention is presented below.

[0081] Other modules maybe included in the financial advisory system 100such as a pension module and a social security module. The pensionmodule may be provided to estimate pension benefits and income. Thesocial security module may provide estimates of the expected socialsecurity income that an individual will receive upon retirement. Theestimates may be based on calculations used by the Social SecurityAdministration (SSA), and on probability distributions for reductions inthe current level of benefits.

[0082] Core Asset Scenario Generation

[0083]FIG. 4 is a flow diagram illustrating core asset class scenariogeneration according to one embodiment of the present invention. Inembodiments of the present invention, core assets include short-term USgovernment bonds, long-term US government bonds, and US equities. Atstep 410, parameters for one or more functions describing statevariables are received. The state variables may include general economicfactors, such as inflation, interest rates, dividend growth, and othervariables. Typically, state variables are described by econometricmodels that are estimated based on observed historical data.

[0084] At step 420, these parameters are used to generate simulatedvalues for the state variables. The process begins with a set of initialconditions for each of the state variables. Subsequent values aregenerated by iterating the state variable function to generate newvalues conditional on previously determined values and a randomly drawninnovation term. In some embodiments, the state variable functions maybe deterministic rather than stochastic. In general, the randomly drawninnovation terms for the state variable functions may be correlated witha fixed or conditional covariance matrix.

[0085] At step 430, returns for core asset classes are generatedconditional on the values of the state variables. Returns of core assetclasses may be described by a function of a constant, previouslydetermined core asset class returns, previously determined values of thestate variables, and a random innovation term. Subsequent values aregenerated by iterating a core asset class function to generate newvalues conditional on previously determined values and a random draws ofthe innovation term. In some embodiments, the core asset class functionsmay be deterministic rather than stochastic. In general, the randomlydrawn innovation terms for the core asset class functions may becorrelated with a fixed or conditional covariance matrix.

[0086] In alternative embodiments, steps 410 and 420 may be omitted andthe core asset class returns may be generated directly in anunconditional manner. A simple example of such a model would be afunction consisting of a constant and a randomly drawn innovation term.

[0087] A preferred approach would jointly generate core asset classreturns based on a model that incorporates a stochastic process (alsoreferred to as a pricing kernel) that limits the prices on the assetsand payoffs in such a way that no arbitrage is possible. By furtherintegrating a dividend process with the other parameters an arbitragefree result can be ensured across both stocks and bonds. Furtherdescription of such a pricing kernel is disclosed in a copending U.S.Pat. No. 6,125,355, assigned to the assignee of the present invention,the contents of which are hereby incorporated by reference.

[0088] Factor Model Asset Scenario Generation

[0089] Referring now to FIG. 5, factor model asset scenario generationwill now be described. A scenario in this context is a set of projectedfuture values for factors. According to this embodiment, the factors maybe mapped onto the core asset factors by the following equation:

r_(it)=α_(i)+β_(1i)ST_Bonds_(t)+β_(2i)LT_Bonds_(t)+β_(3i)US_Stocks_(i)+ε_(i)  (EQ#1)

[0090] where

[0091] r_(it) represents the return for a factor, i, at time t

[0092] β_(ji) represent slope coefficients or the sensitivity of thefactor i to core asset class j

[0093] ST_Bonds_(t) is a core asset class representing the returnsestimated by the pricing module 305 for short-term US government bondsat time t

[0094] LT_Bonds_(t) is a core asset class representing the returnsestimated by the pricing module 305 for long-term US government bonds attime t.

[0095] US_Stocks_(t) is a core asset class representing the returnsestimated by the pricing module 305 for US stocks at time t.

[0096] α_(i) is a constant representing the average returns of factorasset class i relative to the core asset class exposures (“factoralpha”).

[0097] ε_(i) is a residual random variable representing the returns offactor asset class i that are not explained by the core asset classexposures (“residual variance”).

[0098] At step 510, the beta coefficients (also referred to as theloadings or slope coefficients) for each of the core asset classes aredetermined. According to one embodiment, a regression is run to estimatethe values of the beta coefficients. The regression methodology may ormay not include restrictions on the sign or magnitudes of the estimatedbeta coefficients. In particular, in one embodiment of the presentinvention, the coefficients may be restricted to sum to one. However, inother embodiments, there may be no restrictions placed on the estimatedbeta coefficients.

[0099] Importantly, the alpha estimated by the regression is not usedfor generating the factor model asset scenarios. Estimates of alphabased on historical data are extremely noisy because the variance of theexpected returns process is quite high relative to the mean. Based onlimited sample data, the estimated alphas are poor predictors of futureexpected returns. At any rate, according to one embodiment, a novel wayof estimating the alpha coefficients that reduces the probability ofstatistical error is used in the calibration of the factor model. Thisprocess imposes macroconsistency on the factor model by estimating thealpha coefficients relative to a known efficient portfolio, namely theMarket Portfolio. Macroconsistency is the property that expected returnsfor the factor asset classes are consistent with an observed marketequilibrium; that is, estimated returns will result in markets clearingunder reasonable assumptions. The Market Portfolio is the portfoliodefined by the aggregate holdings of all asset classes. It is aportfolio consisting of a value-weighted investment in all factor assetclasses. Therefore, in the present example, macroconsistency may beachieved by setting the proportion invested in each factor equal to thepercentage of the total market capitalization represented by theparticular factor asset class.

[0100] At step 520, a reverse optimization may be performed to determinethe implied factor alpha for each factor based upon the holdings in theMarket Portfolio. This procedure determines a set of factor alphas thatguarantee consistency with the observed market equilibrium. In astandard portfolio optimization, Quadratic Programming (QP) is employedto maximize the following utility function: $\begin{matrix}{{{{E(r)}^{T}X} - \frac{\left( {X^{T}{C(r)}X} \right)}{\tau}},{{u^{T}X} = 1}} & \text{(EQ~~~\#2)}\end{matrix}$

[0101] where,

[0102] E(r) represents expected returns for the asset classes,

[0103] C(r) represents the covariance matrix for the asset classreturns,

[0104] τ, Tau, represents a risk tolerance value,

[0105] X is a matrix representing the proportionate holdings of eachasset class of an optimal portfolio comprising the asset classes, and

[0106] u is a vector of all ones.

[0107] C(r) may be estimated from historical returns data or moreadvantageously may be estimated from projected returns generated by apricing kernel model.

[0108] Inputs to a standard portfolio optimization problem include E(r),C(r), and Tau and QP is used to determine X. However, in this case, X isgiven by the Market Portfolio, as described above, and a reverseoptimization solves for E(r) by simply backing out the expected returnsthat yield X equal to the proportions of the Market Portfolio.

[0109] Quadratic Programming (QP) is a technique for solving anoptimization problem involving a quadratic (squared terms) objectivefunction with linear equality and/or inequality constraints. A number ofdifferent QP techniques exist, each with different properties. Forexample, some are better for suited for small problems, while others arebetter suited for large problems. Some are better for problems with veryfew constraints and some are better for problems with a large number ofconstraints. According to one embodiment of the present invention, whenQP is called for, an approach referred to as an “active set” method isemployed herein. The active set method is explained in Gill, Murray, andWright, “Practical Optimization,” Academic Press, 1981, Chapter 5.

[0110] The first order conditions for the optimization of Equation #2are: $\begin{matrix}{{E(r)} = {{2{C(r)}\frac{X}{\tau}} + {Ku}}} & \left( {{EQ}\quad {\# 3}} \right)\end{matrix}$

[0111] where K is a Lagrange multiplier; hence, knowing the MarketPortfolio and any two values of E(r) (for example, the risk free rateand the return on US equities) the full set of expected returns that areconsistent with the Market Portfolio can be derived. The two values ofE(r) required for the reverse optimization follow from the expectedreturns of the core assets.

[0112] At step 530, factor returns may be generated based upon theestimated alphas from step 520 and the estimated beta coefficients fromstep 510. As many factor model asset scenarios as are desired may begenerated using Equation #1 and random draws for the innovation valueε_(i). A random value for ε_(t) is selected for each evaluation ofEquation #1. According to one embodiment, ε_(t) is distributed as astandard normal variate. In other words ε_(t) is drawn from a standardnormal distribution with a mean of 0 and a standard deviation of 1.

[0113] Advantageously, in this manner, a means of simulating futureeconomic scenarios and determining the interrelation of asset classes isprovided.

[0114] Financial Product Exposure Determination

[0115] As discussed above, one method of determining how a financialproduct behaves relative to a set of factor asset classes is to performreturns-based style analysis. According to one embodiment, returns for agiven financial product maybe estimated as a function of returns interms of one or more of the factor asset classes described above basedon the following equation:

r _(ft)=α_(ft) +S _(f1) r _(1t) +S _(f2) r _(2t) + . . . +S _(fn) r_(nt)+ε_(t)  (EQ #4)

[0116] where,

[0117] α_(ft) is the mean of the left over residual risk (“selectionvariance”) of the financial product return that cannot be explained interms of the factor loadings.

[0118] r_(ft) is the return for financial product f at time t,

[0119] r_(nt) is the return for factor n at time t, and

[0120] ε_(t) is the residual at time t that is unexplained by movementsin the factor returns.

[0121] The financial product exposure determination module 315 computesthe factor asset class exposures for a particular fund via a nonlinearestimation procedure. The exposure estimates, S_(fn), are called stylecoefficients, and are generally restricted to the range [0,1] and to sumto one. In other embodiments, these restrictions may be relaxed (forexample, with financial products that may involve short positions, thecoefficients could be negative). Alpha may be thought of as a measure ofthe relative under or over performance of a particular fund relative toits passive style benchmark.

[0122] At this point in the process, the goal is to take any individualgroup of assets that people might hold, such as a group of mutual funds,and map those assets onto the factor model, thus allowing portfolios tobe simulated forward in time. According to one embodiment, this mappingis achieved with what is referred to as “returns-based style analysis”as described in Sharpe [1992], which is hereby incorporated byreference. Generally, the term “style analysis” refers to determining afinancial product's exposure to changes in the returns of a set of majorasset classes using Quadratic Programming or similar techniques.

[0123]FIG. 6 is a flow diagram illustrating a method of determining afinancial product's exposures to factor asset class returns according toone embodiment of the present invention. At step 610, the historicalreturns for one or more financial products to be analyzed are received.According to one embodiment, the financial product exposure module 315may reside on a server device and periodically retrieve the historicalreturn data from a historical database stored in another portion of thesame computer system, such as RAM, a hard disk, an optical disc, orother storage device. Alternatively, the financial product exposuremodule 325 may reside on a client system and receive the historicalreturn data from a server device as needed. At step 620, factor assetclass returns are received.

[0124] At step 630, QP techniques or the like are employed to determineestimated exposures (the S coefficients) to the factor asset classreturns.

[0125] At step 640, for each financial product, expected future alpha isdetermined for each subperiod of the desired scenario period. Withregards to mutual funds or related financial products, for example,historical alpha alone is not a good estimate of future alpha. That is,a given mutual fund or related financial product will not continue tooutperform/under perform its peers indefinitely into the future. Rather,empirical evidence suggests that over performance may partially persistover one to two years while under performance may persist somewhatlonger (see for example, Carhart, Mark M. “On Persistence in Mutual FundPerformance.” Journal of Finance, March 1997, Volume 52 No. 1,pp.57-82).

[0126] For example, future alpha may depend upon a number of factors,such as turnover, expense ratio, and historical alpha. Importantly, oneor more of these factors may be more or less important for particulartypes of funds. For example, it is much more costly to buy and sell inemerging markets as compared to the market for large capitalization USequities. In contrast, bond turnover can be achieved at a much lowercost, therefore, turnover has much less affect on the future alpha of abond fund than an equity fund. Consequently, the penalty for turnovermay be higher for emerging market funds compared to large cap U.S.equities and bond funds. Improved results may be achieved by taking intoaccount additional characteristics of the fund, such as the fact thatthe fund is an index fund and the size of the fund as measured by totalnet assets, for example.

[0127] According to one embodiment of the present invention, a moresophisticated model is employed for determining future alpha for eachfund:

α_(t)=α_(base)+ρ^(t)(α_(historical)−α_(base))  (EQ #5)

[0128] where,

[0129] α_(base) is the baseline prediction for future Alpha of the fund

[0130] ρ, Rho, governs the speed of decay from α_(historical) toα_(base)

[0131] α_(historical) is Alpha estimated in Equation #4

[0132] According to one embodiment,

α_(base) =C+β ₁Expense_Ratio+β₂Turnover+β₃Fund_Size  (EQ #6)

[0133] where the parameters are estimated separately for each of fourdifferent classes of funds: US equity, foreign equity, taxable bond,nontaxable bond. These parameters may be estimated using conventionaleconometric techniques, such as ordinary least squares (OLS). Accordingto one embodiment, Rho is estimated by first calculating historicaldeviations from α_(base) (“residual alpha”) and then estimating Rho asthe first order serial correlation of the residual alpha series.

[0134] Portfolio Optimization

[0135] Portfolio optimization is the process of determining a set offinancial products that maximizes the utility function of a user.According to one embodiment, portfolio optimization processing assumesthat users have a mean-variant utility function, namely, that peoplelike having more wealth and dislike volatility of wealth. Based on thisassumption and given a user's risk tolerance, the portfolio optimizationmodule 340 calculates the mean-variance efficient portfolio from the setof financial products available to the user. As described above,constraints defined by the user may also be taken into consideration bythe optimization process. For example, the user may indicate a desire tohave a certain percentage of his/her portfolio allocated to a particularfinancial product. In this example, the optimization module 340determines the allocation among the unconstrained financial productssuch that the recommended portfolio as a whole accommodates the user'sconstraint(s) and is optimal for the user's level of risk tolerance.

[0136] Prior art mean-variant portfolio optimization traditionallytreats the problem as a single period optimization. Importantly, in theembodiments described herein, the portfolio optimization problem isstructured in such as way that it may explicitly take into account theimpact of different investment horizons and the impact of intermediatecontributions and withdrawals. Further the problem is set up so that itmay be solved with QP methods.

[0137] Referring now to FIG. 7, a method of portfolio optimizationaccording to one embodiment of the present invention will now bedescribed. At step 710, information regarding expected withdrawals isreceived. This information may include the dollar amount and timing ofthe expected withdrawal. At step 720, information regarding expectedfuture contributions is received. According to one embodiment, thisinformation may be in the form of a savings rate expressed as apercentage of the user's gross income or alternatively a constant orvariable dollar value may be specified by the user.

[0138] At step 730, information regarding the relevant investment timehorizon is received. In an implementation designed for retirementplanning, for example, the time horizon might represent the user'sdesired retirement age.

[0139] At step 740, information regarding the user's risk tolerance,Tau, is received.

[0140] At step 750, the mean-variance efficient portfolio is determined.According to one embodiment, wealth in real dollars at time T isoptimized by maximizing the following mean-variance utility function bydetermining portfolio proportions (X_(i)): $\begin{matrix}{U = {{E\left( W_{T} \right)} - \frac{{Var}\left( W_{T} \right)}{\tau}}} & \text{(EQ~~~\#7)}\end{matrix}$

[0141] where for a given scenario,

[0142] E( W_(T))is the expected value of wealth at a time T

[0143] Var( W_(T))is the variance of wealth at time T

[0144] τ is the user's risk tolerance $\begin{matrix}{W_{T} = {{X_{1}{\sum\limits_{t = 0}^{T - 1}{C_{t}{\prod\limits_{j = {t + 1}}^{T}\left( {1 + R_{j1}} \right)}}}} + \ldots + {X_{n}{\sum\limits_{t = 0}^{T - 1}{C_{t}{\prod\limits_{j = {t + 1}}^{T}\left( {1 + R_{jn}} \right)}}}} + g}} & \text{(EQ~~~\#8)}\end{matrix}$

[0145] where,

[0146] X_(i) represents the recommended constant proportion of each netcontribution that should be allocated to financial product i.

[0147] C_(t) represents the net contribution at time t,

[0148] R_(ji) represents the expected returns for financial product i inyear j,

[0149] n is the number of financial products that are available foroptimization,

[0150] g is the value of constrained assets for a given scenario,

[0151] The product of gross returns represents the compounding of valuesfrom year 1 to the horizon. Initial wealth in the portfolio isrepresented by contribution C₀.

[0152] Importantly, the financial product returns need not representfixed allocations of a single financial product. Within the context ofthe optimization problem, any individual asset return may be composed ofa static or dynamic strategy involving one or more financial products.For example, one of the assets may itself represent a constantre-balanced strategy over a group of financial products. Moreover, anydynamic strategy that can be formulated as an algorithm may beincorporated into the portfolio optimization. For example, an algorithmwhich specifies risk tolerance which decreases with the age of the usercould be implemented. It is also possible to incorporate path dependentalgorithms (e.g., portfolio insurance).

[0153] According to Equation #8, contributions are made from the currentyear to the year prior to retirement. Typically, a contribution made attime t will be invested from time t until retirement. An exception tothis would be if a user specifies a withdrawal, in which case a portionof the contribution may only be held until the expected withdrawal date.

[0154] An alternative to the buy and hold investment strategy assumedabove would be to implement a “constant mix” investment strategy orre-balancing strategy. For purposes of this example, it is assumed thatthe recommended fixed target asset-mix will be held in an account foreach year in the future. Therefore, each year, assets will be boughtand/or sold to achieve the target. Let f_(i) be the fraction of accountwealth targeted for the i-th asset, then the sum of the fractions mustequal one.

[0155] In the following “evolution” equations, nominal wealthaggregation is modeled for a single taxable account from the currenttime t=0 to the time horizon t=T. It is assumed that “N” assets are inthe account, labeled by the set of subscripts {i=1, . . . , N}. Thesuperscripts minus and plus are used to distinguish between the valuesof a variable just before, and just after, “settlement”. The settlement“event” includes paying taxes on distributions and capital gains,investing new contributions, buying and selling assets to achieve theconstant mix, and paying load fees. For example, W⁺(t) is the totalwealth invested in all assets just after settlement at time “t”. Theevolution equations for the pre- and post-settlement values, the“dollars” actually invested in each asset, are: $\begin{matrix}{{W_{i}^{-}(t)} = \left\{ \begin{matrix}{\quad {{W_{i}^{-}(0)},}} & {\quad {{t = 0},}} \\{\quad {{{\left\lbrack {1 + {R_{i}(t)}} \right\rbrack \cdot {W_{i}^{*}\left( {t - 1} \right)}} - {{k_{i}(t)}}},}} & {\quad {{0 < t \leq T},}}\end{matrix} \right.} & \left( {19a} \right) \\{{W_{i}^{+}(t)} = \left\{ \begin{matrix}{\quad {f_{i} \cdot {W^{+}(t)}}} & {\quad {{0 \leq t < T},}} \\{\quad {0,}} & {\quad {t = {T.}}}\end{matrix} \right.} & \text{(19b)}\end{matrix}$

[0156] In the above equation, the double-bar operator ∥ ∥ is equal toeither its argument or zero, whichever is greater. From Eq.(19a), we seethat the pre-settlement value at any time (after the initial time) isjust the gross return on the post-settlement value of the previous timeless the “positive-part” of any distribution, i.e. the “dividend”. Here,k₁(t) is the portion of the return of the i-th asset that isdistributed, and R_(i)(t) is the total nominal return on the i-th assetin the one-year period [t-1, t]. We also assume that an initial,pre-settlement value is given for each asset. Eq.(19b) defines thepost-settlement value in terms of the asset's constant mix and the totalaccount value after settlement. Since we “cash-out” the portfolio at thetime horizon, the final amount in each asset at t=T is zero. The pre-andpost-settlement, total values are governed by the pair of equations:$\begin{matrix}{{{W^{-}(t)} = {\sum\limits_{i = 1}^{N}{W_{i}^{-}(t)}}},{0 \leq t \leq T},} & \text{(19c)} \\{{{W^{+}(t)} = {{W^{-}(t)} + {C(t)} + {D(t)} - {L(t)} - {S(t)}}},{0 \leq t \leq {T.}}} & \text{(19d)}\end{matrix}$

[0157] In Eq.(19), C(t) is the nominal contribution to the account attime “t”, D(t) is the total of all distributed “dividends”, L(t) is the“leakage”, the total amount paid in loads to both rebalance and toinvest additional contributions, and S(t) is the “shrinkage”, the totalamount paid in taxes on distributions and capital gains. We note thatW⁺(T) is the final horizon wealth after all taxes have been paid. Thevalue of D(t), the total of all distributed dividends, is the sum of thepositive distributions: $\begin{matrix}{{{D(t)} = {\sum\limits_{i = 1}^{N}{{k_{i}(t)}}}},{0 \leq t \leq {T.}}} & \text{(19e)}\end{matrix}$

[0158] Similarly, the “leakage” L(t) is the total amount of dollars paidin loads, and L_(i)(t) is the number of dollars paid in loads on justthe i-th asset. These individual loads depend on l_(i), the front-endload fee (a rate) on the i-th asset. $\begin{matrix}{{{L_{i}(t)} = {{\left\lbrack {l_{i}/\left( {1 - l_{i}} \right)} \right\rbrack \cdot {{{W_{i}^{+}(t)} -}}}{k_{i}(t)}{{- {W_{i}^{-}(t)}}}}},{0 \leq t \leq {T.}}} & \text{(19f)} \\{{{L(t)} = {\sum\limits_{i = 1}^{N}{L_{i}(t)}}},{0 \leq t \leq {T.}}} & \text{(19g)}\end{matrix}$

[0159] If there is a short-term loss (negative distribution), the loadfee paid on an asset's purchase is just a fixed fraction of the purchaseprice.^(i) Then there is a short-term gain (positive distribution), wecan re-invest any part of it without load fees, and pay fees only onpurchases in excess of the gain. Note that at the horizon, we“cash-out”, and don't pay any load fees.

[0160] The equation for the “shrinkage” S(t), the total amount paid intaxes, has two terms. The first term is the tax on distributions and ismultiplied by the marginal tax-rate; $\begin{matrix}{{{S(t)} = {{\tau_{m} \cdot {\sum\limits_{i = 1}^{N}{k_{i}(t)}}} + {\tau_{cg} \cdot {\sum\limits_{i = 1}^{N}{\left\lbrack {1 - {{B_{i}\left( {t - 1} \right)}/{W_{i}^{-}(t)}}} \right\rbrack \cdot {{{W_{i}^{-}(t)} - {W_{i}^{+}(t)}}}}}}}},{0 \leq t \leq {T.}}} & \text{(19h)}\end{matrix}$

[0161] the second term is the tax on capital gains and is multiplied bythe capital gains tax-rate.

[0162] In Eq.(19 h), the capital gains tax depends on the basisB_(i)(t), the total of all after-tax nominal-dollars that have beeninvested in the i-th asset up to time “t”. Note that there can be eithera capital gain or loss. The double-bar operator ensures that capitalgains are triggered only when there is a sale of assets. At the horizon,we sell all assets, and automatically pay all taxes. The basis B_(i)(t),evolves according to the following recursion equation: $\begin{matrix}{{B_{i}(t)} = \left\{ \begin{matrix}{\quad {{B_{i}(0)},}} & {\quad {{t = 0},}} \\{\quad {{B_{i}\left( {t - 1} \right)} + {{{W_{i}^{+}(t)} - {W_{i}^{-}(t)}}} + {L_{i}(t)}}} & \quad \\{{\left. \quad {{- {B_{i}\left( {t - 1} \right)}}/{W_{i}^{-}(t)}} \right\rbrack \cdot {{{W_{i}^{-}(t)} - {W_{i}^{+}(t)}}}},} & {\quad {0 \leq t \leq {T.}}}\end{matrix} \right.} & \text{(19i)}\end{matrix}$

[0163] Note that all new purchases are made with after-tax dollars, andadd to the basis; all sales decrease the basis. Further, any load paidto purchase an asset adds to the basis. We assume that the initial basisB_(i)(0) of an asset is either given, or defaults to the initial,pre-settlement value so that the average basis is initially equal toone.

[0164] A “constitutive” equation for k_(l)(t) is needed to complete oursystem of equations. Short-term distributions depend on the “type” ofasset; here we model mutual funds: $\begin{matrix}{{k_{i}(t)} = \left\{ \begin{matrix}{\quad {{k_{i}(0)},}} & {\quad {{t = 0},}} \\{\quad {{\kappa_{i} \cdot {R_{i}(t)} \cdot {W_{i}^{+}\left( {t - 1} \right)}},}} & {\quad {0 < t \leq {T.}}}\end{matrix} \right.} & \text{(20a)}\end{matrix}$

[0165] Often, we set the initial distribution to zero, and assume thatthe asset's initial pre-settlement value has already accounted for anynon-zero, initial value. We note that the distribution is proportionalto the amount of wealth at “stake” during the prior-period. For mutualfunds, we assume that the distribution is a fraction κ_(i) of theprior-period's total return, and therefore is also proportional toR_(i)(t). Note that the distribution in Eq.(20a) can be a gain(positive) or a loss (negative). In contrast, the constitutive equationfor stocks takes the form: $\begin{matrix}{{k_{i}(t)} = \left\{ \begin{matrix}{{k_{i}(0)},} & {{t = 0},} \\{\kappa_{i} \cdot \left\lbrack {{1 + {{R_{i}(t)} \cdot {W_{i}^{+}\left( {t - 1} \right)}}},} \right.} & {0 < t \leq {T.}}\end{matrix} \right.} & \text{(20b)}\end{matrix}$

[0166] For stocks, the proportionality constant κ_(i) models a constantdividend “yield”, and the distribution is always a gain (non-negative).For stocks (mutual funds), the distribution is proportional to the gross(simple) return.

[0167] Before we leave this section, a word on 401(k) plans and IRA's(with no load funds). For these accounts, the loads and taxes areignored, and there is no basis in the asset. At “settlement”, the userjust re-balances their account. The evolution equations for theseaccounts is trivial in comparison to the equations for a general taxableaccount:

W _(i) ⁺(t)=f _(i) ·W ⁺(t),0≦t ≦T,  (21a)

[0168] $\begin{matrix}{{W^{+}(t)} = \left\{ \begin{matrix}{{W^{+}(0)},} & {t = 0} \\{{{\left( {1 + {\sum\limits_{i = 1}^{N}\quad {f_{i} \cdot {R_{i}(t)}}}} \right) \cdot {W^{+}\left( {t - 1} \right)}} + {C(t)}},} & {0 < t \leq {T.}}\end{matrix} \right.} & \text{(21b)}\end{matrix}$

[0169] At the time horizon T, the total wealth in a non-taxable accountis just W⁺(T). This is a pre-withdrawal total value. When retirementwithdrawals are made from a tax-free account, they are taxed at theclient's average tax-rate, τ_(a). Therefore, the “after-tax” equivalentvalue is equal to “pre-tax” wealth W⁺(T) times the tax factor (1−τ_(a)).

[0170] How do we aggregate taxable and non-taxable accounts to get totalportfolio wealth? We choose non-taxable accounts as a baseline. If allthe funds in a non-taxable account were converted to an annuity, and theannuity payments were taken as withdrawals, then the withdrawals wouldmimic a salary subject to income taxes. This is precisely the client'spre-retirement situation. Before aggregating a taxable account, we scaleits “after-tax” value to this baseline using the formula:

W _(baseline) =W _(after-tax)/(1−τ_(a)).  (22)

[0171] Essentially, the baseline equivalent is obtained by grossing upvalues using the average tax-rate.

[0172] The evolution equation variables appear “implicitly” in therecursion relations. Hence, we need to “iterate” at each time step tosolve for “explicit” variable values.^(1i) We illustrate this processwith an example. Consider the simple case where there are nodistributions, contributions, or taxes; just loads, and a constant-mixstrategy. Here, the evolution equations simplify to a single equationfor the total, after-settlement wealth. $\begin{matrix}{{W^{+}(t)} = {{{{W^{+}\left( {t - 1} \right)} \cdot {\sum\limits_{i = 1}^{N}\quad {f_{i} \cdot \left\lbrack {1 + {R_{i}(t)}} \right\rbrack}}} - {\sum\limits_{i = 1}^{N}\quad {f_{i} \cdot \left\lbrack {l_{i}/\left( {1 - l_{i}} \right)} \right\rbrack \cdot {{{W^{+}(t)} - {\left\lbrack {1 + {R_{i}(t)}} \right\rbrack \cdot {W^{+}\left( {t - 1} \right)}}}} \cdot {W^{+}(t)}}}}:}} & (23)\end{matrix}$

[0173] Note, we only know W⁺(t) as an implicit function of W⁺(t−1), butgiven a guess for its value, we can refine the guess by substituting itinto the right-side of Eq.(23).

[0174] It's instructive to re-write Eq.(23) as the pair of equations interms of an “effective” return R_(e)(t):

W ⁺(t)=[1+R _(e)(t)]·W ⁺(t−1),  (24a)

[0175] $\begin{matrix}{{R_{e}(t)} = {{\sum\limits_{i = 1}^{N}\quad {f_{i} \cdot {R_{i}(t)}}} - {\sum\limits_{i = 1}^{N}\quad {f_{i} \cdot \left\lbrack {l_{i}/\left( {1 - l_{i}} \right)} \right\rbrack \cdot {{{{R_{e}(t)} - {R_{i}(t)}}}.}}}}} & \text{(24b)}\end{matrix}$

[0176] Eq.(24a) is the evolution equation for a single asset with theeffective return. Eq.(24b) is an implicit equation for the effectivereturn R_(e)(t) in terms of the asset returns R_(i)(t). We solve for theeffective return using iteration. When the loads are equal to zero, asexpected, the effective return is just a weighted-average of the assetreturns. Even when the loads are not zero, this average return is a goodinitial guess for the iteration procedure. In fact, using the averagereturn as the initial guess and iterating once yields the followingexplicit approximation for the effective return: $\begin{matrix}{{{R_{wgt}(t)} = {\sum\limits_{i = 1}^{N}\quad {f_{i} \cdot {R_{i}(t)}}}},} & \text{(25a)} \\{{R_{e}(t)} \approx {{R_{wgt}(t)} - {\sum\limits_{i = 1}^{N}\quad {f_{i} \cdot l_{i} \cdot {{{{R_{wgt}(t)} - {R_{i}(t)}}}.}}}}} & \text{(25b)}\end{matrix}$

[0177] Eq.(25b) is consistent with our intuition, and agrees well withhigher order iterates.

[0178] To determine the mutual fund input moments we must firstcalculate the kernel moments. This procedure calculates successiveannual kernel moments and averages the result. The resulting mean andcovariance matrix is then utilized by the reverse optimization procedureand also as an input into the optimization procedure.

[0179] To calculate analytic core moments, first we must describe thewealth for each core asset for an arbitrary holding period. For each ofthe core assets, the resulting wealth from an arbitrary investmenthorizon can be written as: [Note, this is an approximation for equities]$W_{t,T} = {\exp \left\{ {{\sum\limits_{j = t}^{T - 1}\quad a} + {bX}_{j + 1} + {c\quad \pi_{j + 1}} + {d\quad \delta_{j + 1}} + {eX}_{j} + {f\quad \pi_{j}} + {g\quad \delta_{j}}} \right\}}$

[0180] Where: a, b, c, d, e, f, g = Constants X_(j) = Real rate in yearj II_(j) = Inflation rate in year j δ_(j) = Dividend growth rate in yearj

[0181] The expectation of wealth for any of the core assets giveninformation at time zero is then:${E_{0}W_{t,T}} = {^{a{({T - t})}}E_{0}^{{\sum\limits_{j = 1}^{T - 1}\quad {eX}_{j}} + {bX}_{j + 1}}E_{0}^{{\sum\limits_{j = 1}^{T - 1}\quad {f\quad \pi_{j}}} + {c\quad \pi_{j + 1}}}E_{0}^{{\sum\limits_{j = 1}^{T - 1}\quad {g\quad \delta_{j}}} + {d\quad \delta_{j + 1}}}}$

[0182] Since X, Π, and δ are independent, we can deal with each of theseexpectations separately. For example, consider the contribution in theabove equation from inflation. The summation can be rewritten as:${E_{0}\exp \left\{ {{\sum\limits_{j = t}^{T - 1}\quad {f\quad \pi_{j}}} + {c\quad \pi_{j + 1}}} \right\}} = {E_{0}\exp \left\{ {{f\quad \pi_{t}} + \left( {\sum\limits_{j = {t + 1}}^{T - 1}\quad {\left( {f + c} \right)\pi_{j}}} \right) + {c\quad \pi_{T}}} \right\}}$

[0183] Next, we need to use iterated expectations to determine thisexpectation. We can write the expectation at time zero as the repeatedexpectation over the various innovations. For example, the equation forinflation can be rewritten as: $\begin{matrix}{{E_{0}\exp \left\{ {{f\quad \pi_{t}} + \left( {\sum\limits_{j = {t + 1}}^{T - 1}\quad {\left( {f + c} \right)\pi_{j}}} \right) + {c\quad \pi_{T}}} \right\}} = \quad {E_{ɛ_{1}}E_{ɛ_{2}}\quad \ldots \quad E_{ɛ_{T}}\exp \left\{ {{f\quad \pi_{t}} +} \right.}} \\{\quad {\left( {\sum\limits_{j = {t + 1}}^{T - 1}\quad {\left( {f + c} \right)\pi_{j}}} \right) + \left. c\quad \pi_{T} \right\}}} \\{= \quad {E_{ɛ_{1}}E_{ɛ_{2}}\quad \ldots \quad E_{ɛ_{T - 1}}\exp \left\{ {{f\quad \pi_{t}} +} \right.}} \\{\quad {\left. \left( {\sum\limits_{j = {t + 1}}^{T - 1}\quad {\left( {f + c} \right)\pi_{j}}} \right) \right\}{E_{ɛ_{T}}\left\lbrack ^{c\quad \pi_{T}} \right\rbrack}}}\end{matrix}$

[0184] Assuming inflation follows a modified square root process:

Π_(t)=μ_(π)+_(π)Π_(t−1)+σ_(π){square root}{square root over(∥Π_(t−1)∥)}ε_(t)

[0185] Where ∥ ∥ denotes the Heaviside function${\pi_{t}} \equiv \left\{ \begin{matrix}0 & {if} & \pi_{t} & \leq & 0 \\\pi_{t} & {if} & \pi_{t} & > & 0\end{matrix} \right.$

[0186] Now we recursively start taking the expectations over epsilonstarting at the end and working backward. So:

E _(ε) _(T) [e ^(cΠ) ^(_(T)) ]=E _(ε) _(T) [e ^(cμ) ^(_(π)) ^(+cρ)^(_(π)) ^(Π) ^(_(T−1)) ^(+cσ) ^(_(π))^({square root}{square root over (∥Π _(T−1) ∥)}) ^(ε) ^(_(T)) ]≈e ^(c(μ)^(_(π)) ^(+ρ) ^(_(π)) ^(Π) ^(_(T−1)) ^(+½cσ) ^(_(π)) ² ^(Π) ^(_(T−1)) )

[0187] Where the approximation is due to the Heaviside function.

[0188] Combining this with the above equation yields:${E_{ɛ_{1}}E_{ɛ_{2}}\quad \ldots \quad E_{ɛ_{T - 1}}\exp \left\{ {{f\quad \Pi_{t}} + \left( {\sum\limits_{j = {t + 1}}^{T - 1}{\left( {f + c} \right)\Pi_{j}}} \right)} \right\} {E_{ɛ_{T}}\left\lbrack ^{c\quad \Pi_{T}} \right\rbrack}} = {E_{ɛ_{1}}E_{ɛ_{2}}\quad \ldots \quad E_{ɛ_{T - 2}}\exp \left\{ {{f\quad \Pi_{t}} + \left( {\sum\limits_{j = {t + 1}}^{T - 1}{\left( {f + c} \right)\Pi_{j}}} \right)} \right\} {E_{ɛ_{T - 1}}\left\lbrack ^{{{c\quad \mu_{\pi}} + {{({{c\quad \rho_{\pi}} + {\frac{1}{2}c^{2}\sigma_{\pi}^{2}} + c + f})}\Pi_{T - 1}}})} \right\rbrack}}$

[0189] In general for any time period t, an exponential linear functionof Π has the following expectation:

E _(ε) _(t) [e ^(A) ^(_(j)) ^(+B) ^(_(jΠt)) ]=E _(ε) _(t) [e ^(A)^(_(j)) ^(+B) ^(_(j)) ^((μ) ^(_(π)) ^(+ρ) ^(_(π)) ^(Π) ^(_(t−1)) ^(+σ)^(_(π)) ^(∥Π) ^(_(t−1)) ^(∥ε) ^(_(t)) )]

=e ^(A) ^(_(j)) ^(+B) ^(_(j)) ^(μ) ^(_(π)) ^(+B) ^(_(j)) ^(Π) ^(_(t−1))^((ρ) ^(_(π)) ^(+½σ) ^(_(π)) ² ^(B) ^(_(j)) ⁾

=e ^(A) ^(_(j)) ^(+B) ^(_(j)) ^(μ) ^(_(π)) ^(+(B) ^(_(j)) ^((ρ) ^(_(π))^(+½σ) ^(_(π)) ² ^(B) ^(_(j)) ^())Π) ^(_(t−1))

=e ^(A) ^(_(j−1)) ^(+B) ^(_(j−1)) ^(Π) ^(_(t−1))

[0190] The critical feature is that an exponential linear function of Πremains exponential linear after taking the expectation. This invarianceallows for the backward recursion calculation. Only the constant (A) andthe slope (B) are changing with repeated application of the expectationoperator. The evolution of A and B can be summarized as

A _(J) =A _(J+1) +μ _(π) B _(J+1)

B _(J) =B _(J+1)[ρ_(π)+½σ_(π) ² B _(J+1)]

[0191] In addition, the B_(J) coefficient has to be increased by (c+f)to account for the additional Π_(J) term in the summation. To implementthis recursive algorithm to solve for expected wealth, first define thefollowing indicator variable:${I\left( {t_{1},t_{2}} \right)} = \begin{Bmatrix}1 & {{{if}\quad t_{1}} \leq j \leq t_{2}} \\0 & {Otherwise}\end{Bmatrix}$

[0192] Next, the following algorithm may be employed:

[0193] InitialConditions J=T, A_(T)=0, B_(T)=c

[0194] (1) J=J−1

[0195] (2) A_(J)=A_(J+1)+μ_(π)B_(J+1) B_(J)=B_(J+1)[ρ_(π)+½σ_(π)²B_(J+1)]+c·I(t+1, T−1)+f·I(t, T−1)

[0196] (3) if J=0, End E (W_(t,T))=e^(A) ^(₁) ^(+b) ^(₁) ^(Π) ^(₀)

[0197] (4) Go To (1)

[0198] The same technique applies to X since it is also a square rootprocess. A similar technique can be used to create a recursive algorithmfor the δ component. The only difference is that δ is an AR(1) processinstead of a square root process.

[0199] In particular,

δ_(t)=μ_(δ)+ρ_(δ)δ_(t−1)+σ_(δ)ε_(t)

[0200] For this AR(1) process, the expectation is of the following form.

E _(ε) _(t) [e ^(A) ^(_(j)) ^(+B) ^(_(j)) ^(δ) ^(_(t)) ]=E _(ε) _(t) [e^(A) ^(_(j)) ^(+B) ^(_(j)) ^((μ) ^(_(δ)) ^(+ρ) ^(_(δ)) ^(δ) ^(_(j−1))^(+σ) ^(_(δ)) ^(ε) ^(_(t)) ⁾]

=e ^(A) ^(_(j)) ^(+B) ^(_(j)) ^(μ) ^(_(δ)) ^(+½σ) ^(_(π)) ² ^(B) ^(_(j))^(+B) ^(_(j)) ^(ρ) ^(_(δ)) ^(δ) ^(_(t−1))

=e ^(A) ^(_(j−1)) ^(+B) ^(_(j−1)) ^(δ) ^(_(t−1))

[0201] The evolution of A and B is thus summarized as:

A _(J) =A _(J+1) +B _(J+1)(μ_(δ)+½σ_(δ) ²)

B _(J) =B _(J+1)ρ_(δ)

[0202] The recursive relationship for δ is then:

[0203] InitialConditions J=T, A_(T)=0, B_(T)=d

[0204] (1) J=J−1

[0205] (2) A_(J)=A_(J+1)+B_(J+1)(μ_(δ)+½σ_(δ) ²)B_(J)=B_(J+1)ρ_(δ)+d·I(t+1, T−1)+g·I(t, T−1)

[0206] (3) if J=0, End E (W_(t,T))=e^(A) ^(₁) ^(+B) ^(₁) ^(δ) ^(₀)

[0207] (4) Go To (1)

[0208] This framework for calculating expected wealth can also be usedto calculate the variance of wealth for an arbitrary holding period.From the definition of variance, we have:

V ₀(W _(t,T))=E ₀(W _(t,T) ²)−E ₀(W _(t,T))²

[0209] but $\begin{matrix}{W_{t,T}^{2} = \left\lbrack {\exp \left\{ {{\sum\limits_{j = t}^{T - 1}a} + {bX}_{j + 1} + {c\quad \Pi_{j + 1}} + {d\quad \delta_{j + 1}} + {eX}_{j} + {f\quad \Pi_{j}} + {g\quad \delta_{j}}} \right\}} \right\rbrack^{2}} \\{= {\exp \left\{ {\sum\limits_{j = t}^{T - 1}{2\left( {a + {bX}_{j + 1} + {c\quad \Pi_{j + 1}} + {d\quad \delta_{j + 1}} + {eX}_{j} + {f\quad \Pi_{j}} + {g\quad \delta_{j}}} \right)}} \right\}}}\end{matrix}$

[0210] So the same technique can be used with a simple redefinition ofthe constants to be twice their original values. Similarly, thecovariance between any two core assets can be calculated by simplyadding corresponding constants and repeating the same technique.

[0211] For the current parameter values, the constants for Bills, Bonds,and Equities are: a b c d e F g Bills 0.0077 0 −1 0 1 0.7731 0 Bonds0.0642 −2.5725 −3.8523 0 2.5846 2.9031 0 Equities 0.0331 −2.4062 −3.70694.4431 2.48 2.79 −3.5487

[0212] Above, a methodology was described for calculating core assetanalytic moments for arbitrary horizons. This section describes howthese moments are translated into annualized moments. The proceduredescribed in this section essentially calculates successive annualmoments for a twenty (20) year horizon and computes the arithmeticaverage of these moments. These ‘effective’ annual moments may then beused as inputs into the reverse optimization procedure and theindividual optimization problem.

[0213] For this calculation, first make the following definitions:

[0214] M_(t) ^(j)=Expected return for j^(th) asset over the period t,t+1

[0215] Cov_(t) ^(i,j)=Covariance of returns on asset i with asset j overthe period t,t+1

[0216] These expected returns and covariance are calculated using theformulas described above. The effective annual expected return for assetj is then calculated as:$M^{j} = {\sum\limits_{t = 1}^{T}{\omega_{t}M_{t}^{j}}}$

[0217] Similarly, the effective annual covariance between returns onasset i and returns on asset j are calculated as: (Note, the weights,ω_(t), are between zero and one, and sum to one.)${Cov}^{i,j} = {\sum\limits_{t = 1}^{T}{\omega_{t}{Cov}_{t}^{i,j}}}$

[0218] In one embodiment, this annualizing technique could bepersonalized for a given user's situation. For example, the user'shorizon could specify T, and their level of current wealth and futurecontributions could specify the relevant weights. However for purposesof illustration, the relevant ‘effective’ moments for optimization andsimulation are computed assuming a horizon of 20 years (T=20), and equalweights (i.e. 1/T).

[0219] The techniques described in this section allow for thecalculation of the following effective annual moments: Output parametername Description Units M¹ Bills: expected return Return per year M²Bonds: expected return Return per year M³ Equity: expected return Returnper year Cov^(1,1) Bills: variance of returns (Return per year)²Cov^(2,2) Bonds: variance of returns (Return per year)² Cov^(3,3)Equity: variance of returns (Return per year)² Cov^(1,2) Bills andBonds: covariance (Return per year)² Cov^(1,3) Bills and Equity:covariance (Return per year)² Cov^(2,3) Bonds and Equity: covariance(Return per year)²

[0220] Plan Monitoring

[0221] Exemplary conditions which may trigger an alert of some sort fromthe plan monitoring module 350 were described above. At this point, someof the real world events that may lead to those alert conditions willnow be described. The real world events include the following: (1) afinancial product's style exposure changes, (2) the market value of theuser's assets have changed in a significant way, (3) new financialproducts become available to the user, (4) the risk characteristics ofthe user's portfolio have deviated from the desired risk exposure, or(5) the currently recommended portfolio no longer has the highestexpected return for the current level of portfolio risk (e.g., theportfolio is no longer on the mean-variance efficient frontier). Anefficient frontier is the sets of assets (portfolios) that provide thehighest level of return over different levels of risk. At each point onthe efficient frontier, there is no portfolio that provides a higherexpected return for the same or lower level of risk.

[0222] When a financial product's exposures change it may pull theuser's portfolio off of the efficient frontier. That is, due to a shiftin the investment style of a particular financial product, the portfolioas a whole may no longer have the highest expected return for thecurrent level of risk. According to one embodiment of the presentinvention, if the inefficiency is greater than a predetermined toleranceor if the inefficiency will substantially impact one of the user'sfinancial goals, such as his/her retirement income goal, then the useris notified that he/she should rebalance the portfolio. However, if theinefficiency is within the predefined tolerance then the plan monitoringmodule 350 may not alert the user. In one embodiment, the predefinedtolerance depends upon the impact of the inefficiency on expectedwealth. In addition, the tolerance could depend upon relevanttransaction costs.

[0223] A significant change in the market value of the user's assets mayaffect one or both of the probability of achieving a financial goal andthe current risk associated with the portfolio. In the case that theuser's portfolio has experienced a large loss, the portfolio may nolonger be within a predetermined probability tolerance of achieving oneor more financial goals. Further, as is typical in such situations, therisk associated with the portfolio may also have changed significantly.Either of these conditions may cause the user to be notified thatchanges are required in the portfolio allocation or decision variablesto compensate for the reduction in market value of the portfolio. Alarge increase in the value of the user's portfolio, on the other hand,could trigger an alert due to the increase in the probability ofachieving one or more financial goals or due to the altered riskassociated with the newly inflated portfolio.

[0224] When one or more new financial products become available to theuser, the user may be alerted by the plan monitoring module 350 if, forexample, a higher expected return may be possible at lower risk as aresult of diversifying the current portfolio to include one or more ofthe newly available financial products.

[0225] Having explained the potential effects of some real world eventsthat may trigger alerts, exemplary plan monitoring processing will nowbe described with respect to FIG. 8. At step 810, the data needed forreevaluating the current portfolio and for determining a current optimalportfolio is retrieved, such as the user profile and portfolio datawhich may be stored on the AdviceServer 110, for example. Importantly,the user profile may include investment plan profile information storedduring a previous session, such as the probability of reaching one ormore financial goals, the risk of the portfolio, and the like. Asdescribed above, selected user information on the AdviceServer 110 maybe kept up to date automatically if the financial advisory system 100has access to the record-keeping systems of the user's employer.Alternatively, selected user information may be updated manually by theuser.

[0226] At step 820, a current optimal portfolio is determined, asdescribed above. Importantly, changes to the user database and/orportfolio data are taken into consideration. For example, if one or morenew financial products have become available to the user, portfoliosincluding the one or more new financial products are evaluated.

[0227] At step 830, the current portfolio is evaluated in a number ofdifferent dimensions to determine if any trigger conditions aresatisfied. For example, if the increase in expected wealth, or theincrease in the probability of reaching one or more investment goalsresulting from a reallocation to the current optimal portfolio is abovea predetermined tolerance, then processing will continue with step 840.Additionally, if the risk of the current portfolio is substantiallydifferent from the investment plan profile or if the probability ofachieving one or more financial goals is substantially different fromthe investment plan profile, then processing continues with step 840.

[0228] At step 840, advice processing is performed. According to oneembodiment of the present invention, based upon the user's preferenceamong the decision variables, the system may offer advice regardingwhich decision variable should be modified to bring the portfolio backon track to reach the one or more financial goals with the desiredprobability. In addition, the system may recommend a reallocation toimprove efficiency of the portfolio. An alert may be generated to notifythe user of the advice and/or need for affirmative action on his/herpart. As described above, the alert may be displayed during a subsequentuser session with the financial advisory system 100 and/or the alertsmay be transmitted immediately to the user by telephone, fax, email,pager, fax, or similar messaging system.

[0229] Advantageously, the plan monitoring module 350 performs ongoingportfolio evaluation to deal with the constantly changing data that mayultimately affect the exposure determination process and the portfoliooptimization process. In this manner, the user may receive timely adviceinstructing him/her how to most efficiently achieve one or morefinancial goals and/or maintain one or more portfolio characteristicsbased upon the available set of financial products.

[0230] Exemplary Advice Summary Screen

[0231] The UI 345 attempts to help the user pick the right financialproducts to meet his/her needs in a world where the number of financialproducts and decisions related thereto may be overwhelming. According toone embodiment, the UI 345 helps the user pick the right products byfocusing the user on the relevant decisions and showing the user variousnotions of risk via simulated outcomes that are based upon a set ofrecommended financial products that satisfy the user's current decisionvalues.

[0232]FIG. 9 illustrates an advice summary screen 900 according to oneembodiment of the present invention. According to the embodimentdepicted, the advice summary screen 900 includes three separate areas:(1) an area 910 for decisions, (2) an area 920 for depicting outputvalues (also referred to as results), and (3) an area 930 for depictingrecommended financial products.

[0233] Area 910 organizes all the decisions in one place. While priorart systems, such as retirement calculators, often make the user provideassumptions, data and decisions all in one place, according to theembodiment depicted, the decisions are kept separate. For example, inone embodiment, graphical input mechanisms, such as slider bars aregrouped together in a predefined portion of the display that is separatefrom the output values and the recommended financial products. In thismanner, the user will not confuse the things the user can control andchange (e.g., savings rate or level of savings) and those things theuser cannot change (e.g., inflation, rate of return for a particularfinancial product). Further, area 910 may present a constrained set ofdecisions. That is, only the relevant decisions upon which the userneeds to focus may be presented. Another feature of the presentembodiment is the fact that the decisions are always feasible and insome cases are additionally constrained to be optimal. Calibration ofinput mechanisms is discussed below.

[0234] Importantly, decision variables may vary from implementation toimplementation. For example, in a retirement planning system, decisionvariables might include one or more of: risk, level of savings, andretirement age. In contrast, a mortgage analysis package may includedecision variables such as cost of house, length of mortgage, and amountof down payment. Exemplary input mechanisms for allowing the user tospecify decision variable values are described further below.

[0235] Based upon the decisions, the portfolio optimization module 340produces a recommended set of financial products and the simulationengine projects the outcomes of holding the specific financial productsrecommended. Area 920 organizes all the output values relating to therecommended set of decisions and financial products in one place. Forexample, in one embodiment, graphical representations of the outputvalues are grouped together in a predefined portion of the display thatis separate from the decisions and the recommended financial products.The output values are made available to users to allow them to arrive ata set of financial products that satisfy their objective functions. Forexample, some individuals have a need to have a certain amount of moneyin the future and others may have a need to avoid short-term losses.Generally what is meant by objective function is a criterion that anindividual considers important in making a decision. In variousembodiments of the present invention, the output values may include: thecumulative probability of reaching a predetermined goal, the most likelyvalue of a given portfolio at some future point in time, the financialloss that might occur with a 5% probability within the next 12 months,and various other statistics based on the probability distributionemployed by the simulation engine.

[0236] Different output values may be appropriate for different people.Therefore, by presenting a number of different output values in area920, users are given the ability to focus on whatever output values thatmay appeal to them. In one embodiment, this section of the advice screen900 may be adaptive. That is, a user may select to have displayed one ormore output values that are relevant to satisfying his/her objectivefunction. Importantly, output values may be displayed in various ordersand not all output values need to be displayed concurrently.

[0237] It is appreciated that different output values may also beappropriate for different problems. For example, in a retirementplanning system, it may be desirable to have output values that depictshort- and long-term financial risk and the cumulative probability ofreaching a financial goal. While a mortgage analysis package may includeoutput values such as cash flow, the highest a mortgage payment might bewithin 5 years, the probability of hitting the cap of an adjustable ratemortgage, the probability of paying higher interest costs for aparticular fixed cost mortgage than a particular adjustable ratemortgage, etc.

[0238] Area 930 presents the user with the actions to be taken to getthe results depicted in area 920. For example, an indication ofrecommended financial products may be provided based upon the user'sdecisions. Additionally, recommended proportions of a user's wealth thatshould be allocated to each financial product may be textually and/orgraphically communicated. Another function of area 930 is organizing allthe actions resulting from the decisions in one place. For example, inone embodiment, graphical representations of the recommended financialproducts are grouped together in a predefined portion of the displaythat is separate from the decisions and the output values.

[0239] Areas 910, 920, and 930 may be tied together by the simulationengine and the portfolio optimization module 340. For example, theportfolio optimization module 340 may produce an optimal set offinancial products for a given set of decisions. Further, the simulationengine may connect the decisions to the results by projecting theoutcomes of owning the set of financial products recommended by theportfolio optimization module 340.

[0240] In the embodiment depicted, areas 910, 920, and 930 areconcurrently displayed. In alternative embodiments, however, two of theareas may be displayed concurrently and the third area may be displayedon another screen or at a later time. For example, a visual indicationdepicting input mechanisms for receiving input decisions and a visualindication depicting a set of output values based upon the inputdecisions may be displayed simultaneously thereby allowing the user toobserve updates to the output values in response to changes to one ormore of the input decisions. Then, when the user is satisfied with theoutput values, he/she may view the recommended financial products uponwhich the output values are based.

[0241] Exemplary Decision-Related Functionality

[0242] A. Slider Calibration

[0243] The UI 345 may provide graphical input mechanisms for allowing auser to provide values for one or more decision variable inputs. Asdiscussed earlier, one disadvantage of some prior financial analysisprograms is that the user is often presented with future scenarios thatare not feasible and is therefore free to choose collections offinancial products which are not optimal. That is, the user interfacesdo not constrain the user's input to specific available financialproducts and they do not eliminate combinations of financial productswhich are dominated. By a dominated decision what is meant is a decisionin which the user can absolutely make him/herself better off in onerespect without making him/herself worse off in any other respect. Inembodiments of the present invention, various dominated decisions may beeliminated. For example, the system may assume that the recommendedportfolio should lie on the efficient frontier.

[0244] As a feature of the present embodiment, various positions(settings) of a graphical input mechanism relating to investment riskmay be constrained based upon a set of available financial productsavailable to the user.

[0245]FIG. 10A illustrates an exemplary set of financial products thatmay be available to a user. The financial products, mutual funds in thisexample, may be the investments that are available through an employer's401(k) program, for example. According to one embodiment, the financialproducts may be listed in order of the volatility of their returns. Inthis example, the Vanguard Bond Fund is more volatile than the VanguardMoney Market, the Equity Income Fund is more volatile than both theMoney Market and the Bond Fund, and the Vanguard Small Cap Fund is themost volatile fund of the set.

[0246] Referring now to FIG. 10B, exemplary graphical input mechanismsare depicted. According to one embodiment of the present invention,slider bars are the mechanism by which values regarding decisionvariables are communicated between the simulator and the user. Forexample, the user may modify the current value of a particular decisionvariable by selecting the appropriate slider with an input device andmoving the slider to a new position. According to the embodimentdepicted, the decision variables upon which the simulator's probabilitydistribution is dependent include the user's risk tolerance, the user'ssavings rate, and the user's desired retirement age. Therefore, in thisexample, the UI 345 includes at least three slider bars including a riskslider bar 1000, a savings rate slider bar 1020, and a retirement ageslider bar 1030.

[0247] The risk slider bar includes a left end point 1005, a right endpoint 1015, and a slider 1010. The left end point 1005 represents thelowest risk feasible portfolio and the right end point 1015 representsthe highest risk feasible portfolio. The user may indicate his/her riskpreference to the financial analysis system by positioning the slider1010 anywhere between the left end point 1005 and the right end point1015, inclusive. To assure every position of the risk slider 1010 iswithin the feasible set of risk available to the user, the risk sliderbar 1000 is calibrated based upon the set of financial products that areavailable to the user. Preferably, the simulation module 330additionally keeps the user on the efficient frontier by recommendingonly portfolios of financial products that will result in the highestreturn for a particular level of risk. This means as the user positionsthe risk slider 1010, the simulation module 330 may construct aportfolio from the available set of financial products which has thehighest returns for the specified level of risk. For example, assumingthe risk slider bar 1000 were calibrated to the set of mutual fundsshown in FIG. 10A, then positioning the risk slider 1010 at the left endpoint 1005 would correspond to the highest return portfolio having arisk equivalent to or less than that of the Vanguard Money Market Fund.Similarly, positioning the slider 1010 at the right end point 1015 wouldcorrespond to the highest return portfolio having a risk equivalent toor less than that of the Vanguard Small Cap Fund. Advantageously, inthis manner the UI 345 by way of the risk slider bar 1000 prevents theuser from selecting a level of risk outside of the feasible set of riskthat is actually available to the user.

[0248] It should be appreciated the savings rate slider bar 1020 and theretirement age slider bar 1030 may be similarly constrained to feasiblevalues. For example, the savings rate slider bar 1020 may be constrainedto values between zero and the maximum contribution for a particularaccount type, such as a 401(k). Also, the retirement age slider bar 1030may be constrained to allow values between the user's current age and anupper bound that may be determined with reference to actuarial data, forexample.

[0249] B. Relating Settings of a Risk Input Mechanism to a PredefinedVolatility

[0250] FIGS. 11A-C are helpful for describing the calibration of a riskslider bar 1105 according to one embodiment of the present invention.FIG. 11A depicts a risk slider bar 1105 that may be provided to allow auser to specify a desired level of investment risk, for example. Therisk slider bar 1105 includes a slider 1115, and an indication of thecurrent volatility 1110. According to one embodiment, the volatility ofthe risk slider bar 1105 is expressed as a proportion of a predefinedvolatility, such as the volatility of the Market Portfolio or thevolatility of the average individual investor's portfolio, for example.The Market Portfolio is the portfolio consisting of a value-weightedinvestment in all available assets.

[0251] Returning to the present example, as depicted in FIG. 11A, therisk slider bar 1105 has its slider 1115 positioned in a left mostsetting 1101. The left most setting 1101 corresponds to the volatilityassociated with the lowest volatility mix of financial products in theset of available financial products. In this example, the currentvolatility 1110 of the risk slider 1105 is 0.3×, indicating that thevolatility associated with the current setting of the risk slider bar1115 is 30% of the volatility of the predefined volatility. As discussedbelow, the volatility of the financial products recommended by theportfolio optimization module 340 corresponds to the current setting ofthe risk slider 1101.

[0252] Referring now to FIG. 11B, the risk slider bar 1105 is shown withthe slider 1115 positioned at a midpoint setting 1102. According to thisembodiment, the midpoint setting 1102 corresponds to the predefinedvolatility. Again, the units for risk slider bar 1105 are expressed interms of the volatility of setting 1102 as a proportion of a predefinedvolatility, such as the volatility of the Market Portfolio. In thisexample, the current value 1107 of the setting of the risk slider 1102is 1.0×, indicating that the volatility associated with the currentsetting of slider 1102 is equal to the volatility of the predefinedvolatility.

[0253] Referring now to FIG. 11C, the right most setting 1103 of therisk slider bar 1105 reflects the volatility associated with the highestvolatility mix of financial products in the set of available financialproducts. Again, the units for risk slider bar 1105 are expressed interms of the volatility of setting 1103 as a proportion of a predefinedvolatility, such as the volatility of the Market Portfolio. In thisexample, the current value 1108 of the setting of the risk slider 1105is 2.5×, indicating that the volatility associated with the currentsetting of slider 1103 is 250% of the volatility of the predefinedvolatility.

[0254] Each setting of slider bar 1105 (e.g., 1101, 1102, 1103)corresponds to a unique volatility, and a recommended set of financialproducts whose volatility is equal to that volatility. Advantageously,in the manner described above, the user may choose the desiredvolatility of his/her portfolio of financial products relative to thepredefined volatility. A portfolio having a volatility equal to thepredefined volatility may be chosen by positioning the slider 1115 atthe midpoint 1102. If the user would like the recommended portfolio tobe less volatile than the predefined volatility, then the user mayposition the slider 1115 to the left of the midpoint 1102. Similarly, ifthe user would like the recommended portfolio to be more volatile thanthe predefined volatility, then the user may move the slider 1115 to aposition right of the midpoint 1102. Further, it should be appreciated,the volatility associated with the midpoint 1102 will remain the sameregardless of the composition of the available set of financialproducts.

[0255] While only three different positions of the slider 1115 have beendescribed, it should be appreciated any number of positions may belocated along the risk slider bar 1105 and each position may beassociated with a volatility measure defined by a constant times theportfolio volatility divided by the predefined volatility.

[0256] Exemplary Mechanisms for Communicating Output Values (Results)

[0257] A. Exemplary Manner of Communicating Probabilities from aProbability Distribution

[0258] The chart 1200 of FIG. 12A represents a range of possible valuesof a portfolio of financial products over time. Starting with a set offinancial products that have a current value today, a number ofscenarios of how those financial products might grow taking into accountcontributions and withdrawals may be run by simulation module 330. Theprocess that generates the probability distribution for each time periodmay be a simulation engine, a lookup table that was populated by asimulation engine, or an analytic approximation of the probabilitydistribution that would be generated by the simulation engine. Those ofordinary skill in the art will appreciate that various other mechanismsmay be employed to produce such a probability distribution.

[0259] The vertical axis of the chart 1200 represents dollars and thehorizontal axis represents time, in terms of the user's age, forexample. The chart 1200 further includes an upper line 1205, a lowerline 1215, and a median line 1210. For every point in time, there is aprobability that the value, dollars in this example, will be as high asthe goal 1220.

[0260] In this example, the median line 1210 represents a 50% chance ofthe corresponding dollar value being achieved at a particular point intime. The upper line 1205 may represent an upside 5% tail. The lowerline 1215 may represent a downside 5% tail. Each slice in timerepresents a cross section of the probability distribution. FIG. 12B isa cross section of the chart 1200 which illustrates the probabilitydistribution at a particular slice of time, a₁.

[0261] Returning again to FIG. 12A, there is a higher probability in themiddle range of a particular cross section and a lower probability atthe tails. Ninety percent of the outcomes at a particular time will fallbetween the upper line 1205 and the lower line 1215, inclusive.Exemplary probabilities associated with points x1 through x4 at time a1are as follows: (1) there is a 5% chance of the dollar value being equalto or greater than x1; (2) there is between a 5% and a 50% chance of thedollar value being equal to or greater than x2; (3) there is a 50%chance that the dollar value will be equal to or greater than x3; and(4) there is a 95% chance that the dollar value will be equal to orgreater than x4.

[0262] As one advantage of the present embodiment, rather thanpresenting a misleading binary result or showing the user a depiction ofthe underlying probability 1240, the user interface may communicate thecumulative probability that the user will attain a financial goal in apictorial fashion using certain icons to represent certain levels ofprobability, for example. A one-to-one correspondence may be establishedbetween predetermined levels of probabilities and icons that are used torepresent the predetermined levels of probabilities.

[0263] An exemplary set of icons 1250 is shown in FIG. 12C. A weathertheme is employed by the set of icons 1250 to communicate the likelihoodof achieving the goal 1220. It is appreciated various other themes maybe employed. At any rate, according to this embodiment, icons 1260-1269each include one or more of five basic elements: sky, clouds, sun, sunrays, and a numeric forecast. In one embodiment, the display of thebasic elements may each depend on the likelihood of achieving the goal1220. For example, at certain predefined threshold values variouselements may be included or excluded from the icon to be displayed. Inthe example depicted, the set of icons 1250 range from graphicaldepictions of dark clouds with a dark sky to a bright sun and sun rayswith a bright sky. As the likelihood of achieving the goal 1220increases the weather outlook becomes brighter. In this example, thelowest probability is represented by icon 1260. Icon 1260 includes adark storm cloud and represents less than a 5% chance of the goal beingachieved. Until the probability of achieving the goal reaches 50%, thecloud completely hides the sun. However, the cloud becomes lighter asthe probability increases. Icon 1261 represents that the user has a 10%chance of achieving his/her goal. Icon 1262 represents a 20% chance.Icon 1263 represents a 30% chance of achieving the goal. Icon 1264represents a 40% chance of achieving the goal. Finally, the sun beginsto peek out from behind the cloud in icon 1265 which represents a 50%chance of achieving the goal. Icon 1266 represents a 60% chance ofachieving the goal. Icon 1267 represents a 70% chance of achieving thegoal. Referring to icons 1268 and 1269, once there is an 80% chance orbetter of the goal being achieved, the cloud is no longer present andthe sun's rays become visible. While in this example a weather theme isemployed to communicate probabilities to a user, it is appreciatedvarious other metaphors could be used.

[0264] According to one embodiment of the present invention, as the usermodifies decision variables, such as retirement age, the probabilitydistribution is evaluated and the appropriate icon is displayed to theuser, as described further below.

[0265]FIG. 13 is a flow diagram illustrating a method indicating theprobability of achieving a financial goal according to one embodiment ofthe present invention. At step 1305, a goal is received. The goal may bereceived from the user or it may be retrieved from a user profileestablished during a prior session with the system, for example. Thegoal may represent a financial goal such as a retirement income goal orsome other intermediate goal like saving for a down payment on a home,or a child's college education. In the context of investing, typically aprobability distribution represents the probabilities over time that theportfolio will be worth certain amounts of money.

[0266] At step 1310, values upon which the probability distributiondepend are received. In the context of financial planning software, forexample, these values may include the particular recommended financialproducts, current and projected economic conditions, and user inputsabout the user's level of savings and a time horizon.

[0267] At step 1315, the simulation engine generates a distribution offuture values for future points in time based upon the values receivedat step 1310. According to one embodiment, evaluating the probabilitydistribution may comprise using an analytic approximation of adistribution of simulated values. Alternatively, a table of values maybe generated in advance by a simulation engine, in which case evaluationcomprises retrieving data from the lookup table corresponding to thevalues received at step 1310.

[0268] In this manner, a range of outcomes for a particular time horizonis determined. For example, in the case of evaluating a retirement goal,the time horizon represents the user's stated desired retirement age.Referring again to FIG. 12A, the range of outcomes for a particular timehorizon would represent a cross section of the two-dimensional chart1200, e.g., the values between the lower line 1215 and the upper line1205, inclusive.

[0269] At step 1325, the likelihood of the user achieving the goal isdetermined based on the cumulative probability that meets or exceeds theuser's goal. For example, if the user's goal is to have a specificannual retirement income, then the cumulative probability of achievinggreater than or equal to the specified income is determined.

[0270] At step 1330, an indication is provided to the user of thelikelihood of achieving the goal. According to one embodiment, an icon,corresponding to the likelihood determined at step 1325, is displayed.In this manner, the forecast is summarized in an easily understoodgraphic picture.

[0271] It should be appreciated the feedback mechanism described aboveis also useful in an interactive environment. For example, the visualindication may be changed in real-time as the user manipulates a userinterface mechanism such as a slider bar. By activating an input device(e.g., a mouse, trackball, light pen, or the like), the slider may bemoved to new positions by the user. While the input device is engagedsteps 1310 through 1330 may be repeated for each new position of theslider bar. In this manner, the forecast icon will reflect the forecastat the current position of the slider bar and the user receives feedbackin the form of a changing forecast icon as the slider bar is moved tovarious positions. In an embodiment employing the weather forecast iconsof FIG. 12B, for example, as the slider is moved by the user, theweather changes. When the input device is disengaged, the last displayedicon remains on the display.

[0272] While the embodiment above describes altering the user'sprobability of achieving a goal by changing the time horizon, it shouldbe appreciated there are many other ways of altering the probability.For example, the goal may be raised or lowered, the level of savings maybe increased or decreased, and the investment risk may be modified.

[0273] B. Depiction of Long-Term Risk

[0274]FIG. 14 illustrates a graphical device 1400 which may be employedto communicate long-term financial risk according to one embodiment ofthe present invention. In the embodiment depicted, the graphical device1400 comprises a diamond 1430 having indications of a financial goal1410, an upside retirement income 1420, a projected retirement income1450, and a foundation value 1440. In this example, the financial goal1410 represents a retirement income goal. It should be appreciated thatvarious other financial goals may also be represented such as savingsgoals and other intermediate goals. In this embodiment, the upsideretirement income 1420 represents a 5% chance that the user will havethe retirement income indicated at the retirement age specified. Theprojected retirement income 1450 represents the expected retirementincome based upon the current decision variables. The foundation value1440 represents the 5% worst case retirement income. It is appreciatedthat various other probabilities may be used and that such probabilitiesmay also be user configurable.

[0275] In alternative embodiments, the indication of long-term riskmaybe conveyed by various other graphical devices such as the forecasticons described above or the long-term risk may simply be indicated by anumber and described by accompanying text. Other examples of long-termrisk include, for example, the probability of not achieving a financialgoal, the size of a loss that could happen at some probability oralternatively, the probability of realizing some type of loss. Further,the long-term risk indication may include various value at riskmeasures.

[0276] C. Depiction of Short-Term Risk

[0277]FIG. 15 illustrates a graphical device 1500 that may be used tocommunicate short-term financial risk according to one embodiment of thepresent invention. According to the embodiment depicted, the graphicaldevice comprises a pie chart 1500. In this embodiment, the pie chart1500 represents the user's total wealth and shows the user how much ofit might be lost in a relatively short time period. Pie chart 1500includes two slices, a first slice 1510 and a second slice 1520. Thefirst slice 1510 graphically illustrates the 5% downside chance oflosing the amount corresponding to the size of the first slice 1510. Thesecond slice 1520 graphically illustrates the amount of wealth thatwould remain after such a loss. Again, various other probability valuesmay be employed.

[0278] In alternative embodiments, the indication of short-term risk maybe communicated by various other graphical devices such as the forecasticons described above or the short-term risk may simply be indicated bya number and described by accompanying text.

[0279] Importantly, while exemplary graphical devices for conveyingshort- and long-term financial risk have been illustrated and discussedseparately in FIGS. 14 and 15, area 920 may display multiple aspects offinancial risk and various other output values concurrently on the samescreen as well as individually.

[0280] Area 920 of the advice screen 900 and the UI 345, in general, mayinclude various other output values. For example, a user may find ithelpful to know what the probability of being able to retire during aparticular age range or at a particular age is with a certain retirementincome. Additionally, some users may wish to know what the expectedamount of time to a particular financial goal is or what the worst losspossible is (e.g., the maximum draw down).

[0281] Exemplary Functionality Related to Recommended Financial Products

[0282] A. Real-Time Depiction of Recommended Financial ProductPortfolios

[0283]FIG. 16 is a flow diagram illustrating a method of depictingrecommended financial product portfolios according to one embodiment ofthe present invention. At step 1610, a combination of financial productsthat maximizes the user's utility is determined. This recommended set offinancial products is the set that provides the highest investmentreturn given one or more decision variables specified by the user whichmay include one or more of risk preference, level of savings, and a timehorizon. According to one embodiment, the recommended set of financialproducts is located on an efficient frontier comprising the set ofavailable financial products. An efficient frontier is the space ofrecommended portfolios of financial products that is indexed by one ormore of the decision variables and that is constrained to maximize theuser's utility. Preferably, the efficient frontier determination takesinto account one or more of the level of savings and a time horizon.

[0284] At step 1620, an updated decision variable value is received.According to one embodiment, the user may modify risk, savings, and/orretirement age decision variables by adjusting the position of acorresponding slider. Various other input mechanisms, graphical and/ortextual, may be used, however, to receive decision variable values. Forexample, in alternative embodiments, text entry fields may be providedfor entry of decision variables.

[0285] At step 1630, the simulation module 330 determines the optimalallocation of wealth among the financial products available to the userbased upon the current values for the decision variables.

[0286] At step 1640, the optimal allocation determined in step 1630 ispresented to the user in a graphical form. As above, the graphicalfeedback presented to the user may be provided in real-time as the usermanipulates a graphical input mechanism (e.g., slider bar). For example,while an input device, such as cursor control device 223, is engagedsteps 1620 through 1640 may be repeated for each new position of theselected slider bar. In this manner, the graphical depiction of theoptimal allocation of wealth among the financial products will reflectthe recommendation at the current position of the slider bar and theuser receives feedback in the form of a dynamic graph as the slider baris moved to various positions without deactivating the input device.

[0287] According to one embodiment, the graphical form in which theoptimal financial product allocation is depicted comprises a bar chartas illustrated in FIGS. 17A and 17B. FIG. 17A depicts an exemplary stateof a screen 1700 prior to receipt of an updated decision variable value.According to the embodiment depicted, the screen 1700 includes a barchart 1730 and one or more slider bars such as risk slider bar 1710 forreceiving input decision values. The bar chart 1730 includes a list ofavailable financial products 1720-1727. Each of the financial products1720-1727 are displayed adjacent to a corresponding graphical segment,in this example a bar, having a size (length) representing thepercentage of wealth allocated to that particular financial productaccording to the current recommendation. For example, the currentrecommended allocation of wealth suggests 31% be allocated to financialproduct 1721, 50% to financial product 1722, 7% to financial product1723, and 5% to financial product 1724. In the present example, theavailable financial products 1720-1727 are additionally organized fromtop to bottom in order of increasing volatility of the financial productreturns. Of course, alternative ordering and allocation units, such asdollar amounts, may be called for depending upon the implementation. Therisk slider bar 1710 includes an indication of the current volatility1715 and a slider 1711. In the present state, the risk slider bar 1710has a volatility measure of 0.75×.

[0288] Assuming the user increases the risk, FIG. 17B represents anexemplary state of screen 1700 subsequent to receipt of a new decisionvariable value from the risk slider bar 1710 and after the screen 1700has been updated with the new optimal allocation provided by theportfolio optimization module 340. The risk slider bar 1710 now has avolatility measure of 1.25× and the bar chart 1730 indicates therecommended financial product allocation corresponding to the updatedrisk tolerance value. The new allocation suggests 38% of the user'scontributions be allocated to financial product 1724, 25% to financialproduct 1725, and 37% to financial product 1726.

[0289] While FIG. 17 was described with reference to a specific decisionvariable, risk tolerance, it should be appreciated that the receipt ofnew values of various other decision variables may be handled in asimilar manner.

[0290] B. Modification of the Set of Recommended Financial Products

[0291] It may be the case that the user wants to modify the set ofrecommended financial products. For instance, desiring to hold more orless of a financial product than was recommended. In this event, theuser may modify the recommendation thereby causing the system to updatethe recommended financial products taking into account the user'smodification. Another mechanism, referred to as a user constraint, isprovided by the UI 345 to allow the user to express his/her utilityfunction by modifying the recommended allocation provided by the system.Generally, a user constraint acts as another decision input. Moreparticularly, a user constraint provides the user with the ability toconstrain the holdings of one or more financial products by manipulatingthe recommended financial products. In one embodiment, responsive toreceiving the constraint, the portfolio optimization module 340optimizes the remaining unconstrained financial products such that theportfolio as a whole accommodates the user's constraint(s) and isoptimal for the user's level of risk tolerance. For example, the usermay express his/her desire to hold a certain percentage of a particularfinancial product in his/her portfolio or the user may express his/herpreference that a particular financial product not be held in his/herportfolio. Upon receiving the constraint, the portfolio optimizationmodule 340 determines the allocation among the unconstrained financialproducts such that the recommended portfolio as a whole has the highestutility. Advantageously, in this manner, individuals with utilityfunctions that are different than mean-variant efficient are providedwith a mechanism to directly manipulate the recommended financialproducts to communicate their utility functions.

[0292]FIG. 18 is a flow diagram illustrating a method of updating arecommended portfolio based on a user specified constraint according toone embodiment of the present invention. At step 1810, selection of afinancial product's graphical segment is detected. At step 1820, theselected segment may be resized according to cursor control movement. Atstep 1830, when the resizing is complete, the value associated with thegraphical segment is locked. At step 1840, a new set of financialproducts are recommended. For example, the unconstrained financialproducts may be reoptimized conditional upon user constraints bydetermining an optimal allocation of wealth among the remainingfinancial products. At step 1850, the recommended optimal allocation forthe unconstrained financial products is graphically depicted. It isappreciated that numerous other ways of selecting and manipulating agraphical segment are possible. For example, certain keystrokes on akeyboard such as alphanumeric input device 222 may be employed toactivate various graphical segments and other keys may be used toincrease or decrease the current allocation.

[0293] Again, as above, the graphical feedback presented to the user maybe provided in real-time as the user manipulates the size of the graphicsegment.

[0294]FIG. 19A depicts an exemplary state of a screen 1900 prior toreceipt of a constraint. In this example, screen 1900 includes a barchart 1930 depicting the current allocation of wealth among a set offinancial products 1720-1727. FIG. 19B illustrates an exemplary state ofscreen 1900 after the user has imposed a constraint upon one of thefinancial products and after the screen 1900 has been updated with thenew optimal allocation provided by the portfolio optimization module340. In this example, the user has constrained the allocation of wealthto financial product 1723 to 18%. According to the embodiment depicted,after the graphical segment is locked (step 1830), a lock 1950 isdisplayed to remind the user of the constraint.

[0295] C. Self Explication of Preferences

[0296] By employing the UI components described above, a user maymanipulate decision variables and/or the recommended portfolio andsimultaneously see the impact on the set of outcomes. This process ofself explication of preferences will now briefly be described. Accordingto one embodiment of the present invention, during an initial sessionwith the financial advisory system 100, the user may provide informationregarding risk preferences, savings preferences, current age, gender,income, expected income growth, current account balances, currentfinancial product holdings, current savings rate, retirement age goal,retirement income goals, available financial products, intermediate andlong-term goals, constraints on fund holdings, liabilities, expectedcontributions, state and federal tax bracket (marginal and average). Theuser may provide information for themselves and each profiled person intheir household. This information may be saved in one or more files inthe financial advisory system 100, preferably on one of the servers toallow ongoing plan monitoring to be performed. In other embodiments ofthe present invention additional information may be provided by theuser, for example, estimates of future social security benefits oranticipated inheritances.

[0297] In any event, based on the user's current holdings and the otherdata input by the user, the financial advisory system 100 may providevarious output values. The simulation module 330 may provide aprobability distribution of future portfolio values based on a set ofrecommended financial products and current decisions including, forexample, risk preference, savings rate, and desired retirement age.Additionally, in view of the user's financial goals, the currentdecision variables, and the probability distribution, the simulationmodule 330 may provide an initial diagnosis which may result in a seriesof suggested actions to the user regarding a recommended portfolio thatmaximizes utility conditional upon the current decision variables.

[0298] Once the user has provided the financial advisory system with anynecessary information, an interactive process of modifying the value ofa decision variable, observing the change in one or more output valuesassociated with the current decision variable values, and seeing therecommended financial products that created that particular change maybegin. This process of the system providing feedback and the useradjusting decisions may continue until the user has achieved a desiredset of decision values and financial products that produce a desired setof results. Advantageously, using this interactive approach, the user isnever asked to predict the future with regard to interest rates,inflation, expected portfolio returns, or other difficult to estimateeconomic variables and parameters.

[0299] In the foregoing specification, the invention has been describedwith reference to specific embodiments thereof. It will, however, beevident that various modifications and changes may be made theretowithout departing from the broader spirit and scope of the invention.The specification and drawings are, accordingly, to be regarded in anillustrative rather than a restrictive sense.

What is claimed is:
 1. A method comprising: displaying a set of one or more input objects, the input objects to receive one or more input decisions including an indication of a target retirement age, an indication of a target level of investment risk, and an indication of a retirement income goal; displaying a set of one or more output values, the set of output values including an indication of the probability of achieving the retirement income goal and an indication of the most likely retirement income in current dollars based upon one or more input decisions and a recommended set of financial products; receiving an updated input decision via one or more of the input objects; determining one or more new output values based upon the updated input decision; and refreshing the set of one or more output values to reflect the one or more new output values.
 2. The method of claim 1, wherein a subset of the one or more input objects and a subset of the one or more output values are displayed concurrently on the same screen.
 3. The method of claim 1, wherein the target retirement age is constrained to be feasible.
 4. The method of claim 1, further comprising displaying the recommended set of financial products, the recommended set of financial products conditional on the one or more input decisions.
 5. The method of claim 4, further comprising displaying a recommended allocation of wealth among those of the financial products in the recommended set of financial products.
 6. The method of claim 5, wherein the recommended allocation of wealth is conveyed graphically.
 7. A method of providing an indication to a user of a probability of achieving a financial goal, the method comprising: a. receiving a retirement income goal from the user; b. receiving one or more input decisions from the user, including an indication of a target retirement age and an indication of a target level of investment risk, upon which a probability distribution is dependent, the probability distribution representing a set of possible future portfolio values based upon the one or more input decisions; c. determining the probability of achieving the retirement income goal; and d. displaying the probability of achieving the retirement income goal to the user.
 8. The method of claim 7, wherein the target level of risk is received via a graphical input mechanism.
 9. The method of claim 7, further comprising displaying a recommended set of financial products and a recommended allocation of wealth among the financial products in the set of recommended financial products.
 10. The method of claim 7, wherein the probability of achieving the retirement income goal is graphically communicated.
 11. A method comprising: concurrently displaying input objects in a first portion of a screen, the input objects configured to receive one or more input decisions including level of risk, and a set of one or more output values in a second portion of the screen, the set of output values including the short-term risk associated with reaching a financial goal; receiving an updated input decision via one of the depicted input objects; determining one or more new output values based upon the updated values; and updating the second portion of the screen to reflect the one or more new output values.
 12. The method of claim 11, wherein the short-term risk comprises an indication of the potential financial loss that might occur with a 5% probability within the next 12 months.
 13. The method of claim 11, wherein the one or more output values are graphically communicated.
 14. A method of presenting various aspects of financial risk to a user, the method comprising: receiving an indication of a retirement income goal from the user; receiving one or more inputs including retirement age and/or other decision variables upon which a probability distribution is dependent, the probability distribution representing probabilities over time of the user achieving the retirement income goal; displaying an indication of risk of not achieving the financial goal based upon the probability distribution.
 15. The method of claim 14, wherein the indication of risk of not achieving the retirement income goal comprises an icon.
 16. A method of presenting a recommended allocation of wealth among an available set of financial products, the method comprising: determining a recommended allocation of wealth among one or more financial products of the set of available financial products based upon one or more decision inputs, including an indication of a target level of investment risk; and depicting the recommended allocation of wealth among the one or more financial products of the set of available financial products.
 17. The method of claim 16, wherein the recommended allocation of wealth is graphically depicted.
 18. A method comprising: displaying one or more input objects in a first portion of a first screen, the input objects configured to receive one or more input decisions including a financial goal, from which a recommendation is determined, the recommendation including a recommended allocation of wealth among a set of available financial products; displaying a set of output values in a second portion of the first screen, the set of output values including a probability of achieving the financial goal based upon the recommendation; and graphically depicting the recommended allocation of wealth among the set of available products in a second screen.
 19. The method of claim 18, wherein the one or more input decisions include an indication of a target retirement age.
 20. An apparatus comprising: means for displaying a set of one or more input objects, the input objects to receive one or more input decisions including an indication of a target retirement age, an indication of a target level of investment risk, and an indication of a retirement income goal; means for displaying a set of one or more output values, the set of output values including an indication of the probability of achieving the retirement income goal and an indication of the most likely retirement income in current dollars based upon one or more input decisions and a recommended set of financial products; means for receiving an updated input decision via one or more of the input objects; means for determining one or more new output values based upon the updated input decision; and means for refreshing the set of one or more output values to reflect the one or more new output values.
 21. The apparatus of claim 20, further comprising a means for displaying the recommended set of financial products, the recommended set of financial products conditional on the one or more input decisions.
 22. The apparatus of claim 21, wherein the recommended allocation of wealth is conveyed graphically.
 23. A method comprising the steps of: a step for displaying a set of one or more input objects, the input objects to receive one or more input decisions including an indication of a target retirement age, an indication of a target level of investment risk, and an indication of a retirement income goal; a step for displaying a set of one or more output values, the set of output values including an indication of the probability of achieving the retirement income goal and an indication of the most likely retirement income in current dollars based upon one or more input decisions and a recommended set of financial products; a step for receiving an updated input decision via one or more of the input objects; a step for determining one or more new output values based upon the updated input decision; and a step for refreshing the set of one or more output values to reflect the one or more new output values.
 24. The method of claim 23, wherein the target retirement age is constrained to be feasible.
 25. The method of 24, wherein the target level of investment risk is received via a graphical input mechanism.
 26. An apparatus comprising: means for displaying one or more input objects in a first portion of a first screen, the input objects configured to receive one or more input decisions including a financial goal, from which a recommendation is determined, the recommendation including a recommended allocation of wealth among a set of available financial products; means for displaying a set of output values in a second portion of the first screen, the set of output values including a probability of achieving the financial goal based upon the recommendation; and means for graphically depicting the recommended allocation of wealth among the set of available financial products in a second screen.
 27. The apparatus of claim 26, wherein the one or more input decisions includes an indication of a target retirement age.
 28. A method comprising the steps of: a step for displaying one or more input objects in a first portion of a first screen, the input objects configured to receive one or more input decisions including a financial goal, from which a recommendation is determined, the recommendation including a recommended allocation of wealth among a set of available financial products; a step for displaying a set of output values in a second portion of the first screen, the set of output values including a probability of achieving a financial goal based upon the recommendation; and a step for graphically depicting the recommended allocation of wealth among the set of available products in a second screen.
 29. The method of claim 28 wherein the one or more input objects includes a target level of investment risk.
 30. A server comprising: a processor; and a memory coupled with the processor to store a financial advisory system; the processor to send information to a client machine to display on the client machine: one or more input objects in a first portion of a first screen, the input objects configured to receive one or more input decisions including a financial goal, from which a recommendation is determined, the recommendation including a recommended allocation of wealth among a set of available financial products; a set of output values in a second portion of the first screen, the set of output values including a probability of achieving a financial goal based upon the recommendation; and a graphical depiction of the recommended allocation of wealth among the set of available financial products in a second screen.
 31. The server of claim 30, wherein the one or more input objects includes an indication of a target level of investment risk, and an indication of a retirement income goal.
 32. A method comprising: concurrently displaying a set of one or more input objects, the input objects to receive one or more input decisions including an indication of a target retirement age, and an indication of a retirement income goal; and a set of one or more output values, the set of output values including the most likely value at retirement of a portfolio of available financial products previously input by the user; receiving an updated input decision via one or more of the input objects; determining one or more new output values based upon the updated input decision; and refreshing the set of one or more output values to reflect the one or more new output values.
 33. The method of claim 32, wherein the target retirement age is constrained to be feasible. 